"Let X be a discrete random variable that is uniformly distributed over the set of integers in the range [
a
,
b
]
, where a and b are integers with a < 0 < b. Find the PMF of the random variables Y
=
max
{
0
,
X
}
and W
=
min
{
0
,
X
}
."

Answers

Answer 1

The PMF of Y=max{0,X} is P(Y=k) = (b-k+1)/(b-a+1) for k = 0,1,2,...,b and P(Y=k) = 0 for all other values of k.

The PMF of W=min{0,X} is P(W=k) = (k-a+1)/(b-a+1) for k = a,a+1,a+2,...,0 and P(W=k) = 0 for all other values of k. This is because for Y, the probability of X taking a certain value decreases as that value gets larger, but for W, the probability of X taking a certain value increases as that value gets more negative.

Therefore, the PMF for Y will have a peak at k=0 and decrease as k increases, while the PMF for W will have a peak at k=a and decrease as k becomes more negative.

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Related Questions

10 points please help me!!!

Answers

Step-by-step explanation:

16-19 -> 3 (16, 17, 19)20-23 -> 1 (21)24-27 -> 3 (24, 26, 26)28-31 -> 4 (28, 29, 30, 31)32-35 -> 5 (32, 33, 34, 34, 35)

check out the pic first

Answers

Answer: (0, 16)

Step-by-step explanation:

y = mx + c

c is the y intercept

from the equation, c = 16

(it's not exactly mx but you don't need to solve for x)

Question 12
From the given graph, use two points to write an equation in point-
slope form and then change to slope-intercept form.
Step 1: Use the two points to find the slope.
Step 2: Use the slope and one point to complete point-slope form.
y-y₁ = m(x-x₁)
Step 3: Change point-slope form into slope intercept form by solving
for y. Show your work!
y=mx+b

Answers

1eg
slope=819 plus 329

Find the area of the figure. ​

Answers

Answer:

60 ft^2

Step-by-step explanation:

60ft
Hope this helps if not I’m sorry.

Select the equivalent expression. 2^-4 = ?​

Answers

Answer:

1/16

Step-by-step explanation:

This means 1/2x2x2x2  = 1/16

Nina thought of a number. she added 24 , tripled the result, subtracted 18 , multiplied the result by 2 and got 120 . what was nina's number?

Answers

Answer:

Step-by-step explanation:

If we subtract 3 from the unknown number, we get just as much as if we subtracted 7 from the unknown number and we multiplied the result by 2

At 3:20, what is the measure in degrees of the lesser angle formed by the hour hand and the minute hand

Answers

Answer: 30 degrees

Step-by-step explanation:

The probability is .80 that a standard normal random variable is between -z and +z. The value of z is approximately:________

Answers

The z value for the probability in the standard normal table is 1.29.

In this question,

Z-Score, also known as the standard score, indicates how many standard deviations an entity is, from the mean. A standard normal table (also called the unit normal table or z-score table) is a mathematical table for the values of ϕ, indicating the values of the cumulative distribution function of the normal distribution.

The value of probability is 0.80

A standard normal random variable is between -z and +z, So

P(-z < 0 < z) = 0.80

⇒ 2P(0 < z) = 0.80

⇒ P(0 < z) = [tex]\frac{0.80}{2}[/tex]

⇒ P(0 < z) = 0.40

From the standard normal table, z value for the probability 0.40 is

⇒ z = 1.29

Thus P(0 < 1.29) = 0.40

Hence we can conclude that the z value for the probability in the standard normal table is 1.29.

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A bag contains lettered tiles. the theoretical probability of choosing a vowel is 40%. the bag contains 78 consonants. how many tiles are in the bag?

Answers

The total number of ties present in the bag are 130.

What is probability?

Calculating or estimating how likely something is to occur is what probability is all about. The likelihood of an event occurring can be expressed using words like "certain," "impossible," or "probable."

Formula for probability is -

Probability(Event) = Favourable Outcomes/Total Outcomes

It P(E) is the probability for occurring any event.

'x' be the favourable outcome.

'n' be the total outcome.

Then,

P(E) = x/n.

Calculation for the total tiles present the bag.

The probability of choosing a vowel is 40% = 0.4.

Then, the probability of choosing a consonants will be 1 - 0.4 = 0.6 or 60%.

Let P(E) be the probability of the occurrence of the consonants.

Then,

P(E) = total number of consonants/total tiles in the bag.

Let 'T' be the total tiles in the bag.

0.6 = 78/T

T = 78/0.6

T = 130

Therefore, the total tiles present in the bag are 130.

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find the value of x from the figure

Answers

Answer:

x = 30

Step-by-step explanation:

110 and 3x - 20 are supplementary angles, sum to 180° , then

110 + 3x - 20 = 180

90 + 3x = 180 ( subtract 90 from both sides )

3x = 90 ( divide both sides by 3 )

x = 30

Answer:

x = 30

Step-by-step explanation:

Please refer to the attached photo. (Apologies for the terrible drawing.)

For this question, you must be clear of the angle properties.

z + 110 = 180 (Sum of Angles on a straight line)

z = 180 - 110 = 70

z = 3x - 20 (Corresponding Angles)

3x - 20 = z

3x - 20 = 70

3x = 70 + 20

3x = 90

x = 90 / 3 = 30

A square pool is surrounded by a paved area that is 2 metres wide. If the area of the paving is 72m2, what is the length of the pool?

Answers

The length of the square pool is 8. 49cm

How to determine the area

Note that the formula for finding the area of a square is given as;

Area = length^2

We have

Area = 72 m²

Substitute into the formula

I^2 = 72

Find the square root of both sides

I= √72

I = 8. 49cm

The length of the square pool given as I is 8. 49cm

Thus, the length of the square pool is 8. 49cm

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What addition/subtraction equation should I put?

Answers

Answer:

7 - 10

Step-by-step explanation:

Because it is -3 and 7 - 10 = -3

The weights of certain machine components are normally distributed with a mean of 7.75 ounces and a standard deviation of 0.07 ounces. Find the two weights that separate the top 4% and the bottom 4%. These weights could serve as limits used to identify which components should be rejected. Round your answer to the nearest hundredth, if necessary.

Answers

The weight that separates the top 4% is x = 7.87 (round nearest hundredth) .

The weight that separates the bottom 4% is x = 7.63 (round nearest hundredth).

What is normal distribution?

The majority of the observations are centred around the middle peak of the normal distribution, which is a continuous distribution of probability that really is symmetrical around in its mean.

The probability for values that are farther from of the mean tapered down equally both in directions.

Now, use z-chart to find the z-value for that separates the top 4% and the bottom 4%.

The values of z = +1.75 and z = -1.75

Let the weight of the machines be 'x'.

Use the formula for z- value

z = (x -  μ)/ σ

Where,

σ  is standard deviation =  0.07 ounces.

μ is mean = 7.75 ounces.

Substitute all the values and calculate the weight.

case 1: when z = +1.75

1.75 = (x - 7.75)/0.07

x  = (1.75×0.07) + 7.75

x = 7.872

x = 7.87 (round nearest hundredth)

case 2: when z = -1.75

-1.75 = (x - 7.75)/0.07

x  = (-1.75×0.07) + 7.75

x = 7.6275

x = 7.63 (round nearest hundredth)

Therefore,

x = 7.87 (round nearest hundredth) is weight which separates top 4%.

x = 7.63 (round nearest hundredth) is weight which separates bottom 4%.

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the diagonal of the rectangle is 15 cm and one of its sides is 9 cm. find the area of the rectangle.

Answers

The area of the rectangle is 108 square centimeters.

Given Information

The following information has been given in the question,

Length of the diagonal of the rectangle, l = 15 cm

Length of one of the sides of the rectangle, a = 9 cm

Let the other side of the rectangle be b.

Finding the Other Side of the Rectangle

According to Pythagoras Theorem,

(hypotenuse)² = (base)² + (perpendicular)²

Applying this theorem in the right-angle triangle formed by the diagonal and 9cm side of the rectangle, we get,

l² = a² + b²  [∵ The diagonal makes the hypotenuse]

(15)² = (9)² + b²

b² = (15)² - (9)²

b² = 225 - 81

b² = 144

b = √144

b = 12 cm

Calculating the Area of the Rectangle

Area of the rectangle, A = a × b

A = 9 × 12

A = 108 cm²

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Drag the tiles to the correct boxes to complete the pairs. Suppose you roll a fair six-sided die. Then you roll a fair eight-sided die. Match each probability to its correct value. the probability that both numbers are odd numbers and their product is greater than 10 the probability that the second number is twice the first number the probability of getting numbers whose sum is a multiple of 4 the probability that the sum of the two numbers is greater than 11 the probability that the second number rolled is less than the first number arrowRight arrowRight arrowRight arrowRight arrowRight

Answers

The probability will be:

Case 1  matches with 5/48.

Case 2 matches with 1/12.

Case 3 matches with 1/4.

Case 4 matches with 1/8.

Case 5 matches with 5/16.

How to illustrate the probability?

We have a total sample space of six-sided die and an eight  sided die.

(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8)

(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8)

(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(3,7),(3,8)  

(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(4,7),(4,8)

(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(5,7),(5,8)

(6,1),(6,2),(6,3),(6,4),(6,5),(6,6),(6,7),(6,8)  

Case 1: The Probability that both numbers are odd numbers and their product is greater than 10. are:  (3,5),(3,7),(5,3),(5,5),(5,7)

And the total number of outcomes are: 48.

The required probability is 5/48.

Case 2: The probability that the second number is twice the first number are:

(1,2),(2,4),(3,6),(4,8)

And the total number of outcomes are 48.

So, the required probability is 1/12.

Case 3: The probability of a number whose sum is a multiple of 4 are:

(1,3),(1,7),(2,2),(2,6),(3,1),(3,5),(4,4),(4,8),(5,3),(5,7),(6,2),(6,6).

And the total number of outcomes are: 48.

The required probability is 12/48 = 1/4

Case 4: The probability that the sum of two numbers is greater than 11.

(4,8),(5,8),(6,7),(6,8),(5,7),(6,6)

And a total number of outcomes are 48.

So, the required probability is 6/48 = 1/8.

Case 5: The probability that the second number rolled is less than the first number are:

(2,1),(3,1),(3,2),(4,1),(4,2),(4,3),(5,1),(5,2),(5,3),(5,4),(6,1),(6,2),(6,3),(6,4),(6,5)

And the total number of outcomes are: 48.

The required probability is 15/48 = 5/16.

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A helicopter is 665 feet above the ground. A girl is looking up at the helicopter to form a line. Her line of sight is 5 feet off the ground. The distance between the girl and the helicopter is 280 feet.

A helicopter flies 665 feet above ground. What is the measure of the angle of depression from the helicopter to the girl’s line of sight? Round to the nearest degree.
23°
25°
65°
67°

Answers

The measure of the angle of depression from the helicopter to the girl’s line of sight is 67 degrees.

What is a right angle triangle?

A right angle triangle has one of its angle as 90 degrees. The sides and angles can be found using trigonometric ratios.

Therefore, angle of depression from the helicopter can be found as follows:

tan x = opposite / adjacent

where

x = angle of depression

Hence,

tan x = 660 / 280

tan x = 2.35714285714

x = tan⁻¹ 2.35714285714

x = 67.1231281953

x = 67°

Therefore, the measure of the angle of depression from the helicopter to the girl’s line of sight is 67 degrees.

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Answer:

D = 67

Step-by-step explanation:

mel cuts a slice of cake if her slice is 4/15 of the cake, what is the central angle of her slice, please give answer in degrees

Answers

Answer:

Below in bold.

Step-by-step explanation:

That would be 4/15 * 360   as there are 360 degrees in a circle

= 96 degrees.

Write as a decimal the number that is exactly halfway between 1 100 and 1 10

Answers

Answer:

605

Step-by-step explanation:

We are starting at 110 and not zero, so I need to find have the distance between 110 and 110 and add that to 110.

110 + 1/2(1100 - 110)  Subtract what is in the parentheses

110 + 1/2(990) Find 1/2 of 990

110 + 495

604

Read the following description of a relationship:
Ron is making a banner by stringing letters on a cord. The cord weighs 8
ounces, and each letter weighs 10 ounces.
Let n represent the number of letters and w represent the weight of the banner.
This relationship can also be shown in a table. Complete the equation that represents the
relationship between n and w

Answers

The equation that represents the relationship between n and w is w = 10n + 8.

How to illustrate the expression?

From the information, Ron is making a banner by stringing letters on a cord and the cord weighs 8

ounces and each letter weighs 10 ounces.

Let represent the number of letters

Let w represent the weight of the banner.

In this case, when n = 6, w = 68 and when n = 7, w = 78.

Therefore, the relationship will be:

w = 10n + 8

To confirm let's use n = 6

10n + 8

10(6) + 8

= 68

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Answer:

Step-by-step explanation:

w=10n+8

Convenience sampling Multiple Choice is the same as simple random sampling. ensures that samples are representative of the population. is an unbiased sampling method. collects sample information from groups that are easy to obtain.

Answers

Option (d) is correct. Convenience sampling collects sample information from easy-to-collect groups.

Given convenient sampling.

Convenience sampling is defined as a method adopted by researchers in which they collect market research data from a pre-existing group of respondents. This is the most commonly used sampling technique because it is extremely fast, simple and economical. In many cases, members are easily accessible to be part of the template. It is non-probability sampling and therefore different from random sampling. Since the samples are taken for convenience, the samples are not always representative of the population and therefore have bias. In this case, people were sampled simply because they were convenient.

Thus, convenience sampling collects sample information from easy-to-collect groups.

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16. c= vλ. If c = 2.998 x 10^8 m/s, v= 4.41 x 10¹4 s-¹; find a value for λ.

Answers

Answer:

6.80 x 10⁻⁷ m

Step-by-step explanation:

You can find the value of λ by inserting the given values into the equation and simplifying.

c = vλ                                                            <----- Given equation

2.998 x 10⁸ m/s = (4.41 x 10¹⁴ s⁻¹)λ               <----- Insert values

6.80 x 10⁻⁷ m = λ                                          <----- Divide both sides by 4.41 x 10¹⁴

(Refer to the attached image)​

Answers

Answer:

D.  10

Step-by-step explanation:

To find the distance between two points, use the distance formula:

Distance between two points

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points}[/tex]

Define the two points:

[tex]\textsf{Let }(x_1,y_1)=(4,-3)[/tex]

[tex]\textsf{Let }(x_2,y_2)=(-4,3)[/tex]

Substitute the two defined points into the distance formula and solve for d:

[tex]\implies d=\sqrt{(-4-4)^2+(3-(-3))^2}[/tex]

[tex]\implies d=\sqrt{(-4-4)^2+(3+3)^2}[/tex]

[tex]\implies d=\sqrt{(-8)^2+6^2}[/tex]

[tex]\implies d=\sqrt{64+36}[/tex]

[tex]\implies d=\sqrt{100}[/tex]

[tex]\implies d=\sqrt{10^2}[/tex]

[tex]\implies d=10[/tex]

Therefore, the distance between the two given points is 10 units.

Formula given by

[tex]\boxed{\sf Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}[/tex]

[tex]\\ \tt{:}\longrightarrow D=\sqrt{(-4-4)^2+(3+3)^2}[/tex]

[tex]\\ \tt{:}\longrightarrow D=\sqrt{8^2+6^2}[/tex]

[tex]\\ \tt{:}\longrightarrow D=\sqrt{10^2}[/tex]

[tex]\\ \tt{:}\longrightarrow D=10units[/tex]

Option D

On purchasing a cell phone, Tia got an offer and got the cell phone for $35\%$ less than the tag price. If she saved $\$140$ on that cell phone. Then price on the tag must be $\$$

Answers

On purchasing a cell phone, Tia got an offer and got the cell phone for 35% less than the tag price. If she saved 140 on that cell phone. Then price on the tag is 400.

Since, the cell pone is sold with 35% discount on it.

Tia got that phone at selling price with 35% discount on tag price. Also, she saved around 140 on buying the cell phone.

Therefore, the discount on the cell phone on the tag price is her saving on buying the cell phone.

Hence,

35% discount on tag price=Saved amount

(35/100)×T=140

where T is the tag price.

T=(140×100)35

T=14000/34

T=400

Therefore, on buying the cell phone with 35% discount on tag price costs around 140. Then the tag price is 400.

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How would you describe the graph for the equation |x| <4?



a.) An open circle on 4 with a solid line drawn to an open circle on -4.
b.) A closed circle on 4 with a solid line drawn to a closed circle on -4.
c.) A closed circle on 4 with a solid line drawn to an open circle on -4.
d.) An open circle on 4 with a solid line drawn to a closed circle on -4.

Answers

Answer:

a.) An open circle on 4 with a solid line drawn to an open circle on -4.

Explanation:

Open circles are used for signs: < and >

Closed circles are used for signs: and

Here in the given expression: |x| < 4

[<] sign is used so open circle is used

If |y| < a then -a < y < a

so here, -4 < x < 4

Both circles should be opened, drawn with a solid line from -4 to 4.

Im very confused about my precourse work for AP environmental science.

The conversion method given on the paper is something I am not used to and I cant seem to find any information about anything like this. I only need help with #3 and #4.

Answers

The computation shows that the values are 64000 acres and 563 metric tons.

How to compute the values?

1. A 100 square mile area of national forest is how many acres?

1 mile square = 640 acres

100 square miles = 100 × 640 = 64000 acres.

2. Fifty eight thousand kilograms of solid waste is equivalent to how many metric tons?

1 metric ton = 103kg

58000 kg = 58000/103 = 563 metric tons

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1. Find the pattern in this sequence. Then write
the next three terms in the sequence.
5,2,1,...

Answers

-1,-3,-4 i think this is the answe

Answer:

-1,-3,-4 it is just subtracting the same amount.

Step-by-step explanation:

A plane can cover 9904 km in 8 hours how mucb distance will it cover in 1 hour?

Answers

In one hour the plane will cover a distance of 1238 km.

What is a linear equation?

A linear equation has one or two variables. No variable in a linear equation is raised to a power greater than 1.No variable is used as the denominator of a fraction. A linear equation is defined as an equation that is written in the form of ax+by=c. When solving the system of linear equations, we will get the values of the variable, which is called the solution of a linear equation.

solving this we will get the valve of Y is x is given.

calculation:-

today distance = 9904 km.

total time is taken = 8 hours.

∴total distance covered in one hour = 9904/8

                                                        = 1238 km.

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solve for x -

[tex] x^{2} + 5x + 6 = 0 \\ \\ [/tex]

ty! :)​

Answers

Hello,

x² + 5x + 6 = 0

a = 1 ; b = 5 ; c = 6

∆ = b² - 4ac = 5² - 4 × 1 × 6 = 25 - 24 = 1 > 0

2 solutions :

[tex] x_{1} = \frac{ - b - \sqrt{\Delta} }{2a} = \frac{ - 5 - 1}{2 \times 1} = \frac{ - 6}{2} = - 3[/tex]

[tex]x_{2} = \frac{ - b + \sqrt{\Delta} }{2a} = \frac{ - 5 + 1}{2 \times 1} = \frac{ - 4}{2} = - 2[/tex]

S = { -3 ; -2}

When solving an equation, Anne's first step is shown below. Which property justifies
Anne's first step?

Answers

The justification used is multiplicative property of equality because both sides are multiplied by the same value

Solving linear equations

Given the expression below

-1/3(4x^2 - 3) - 3 = 5x^2 - 2

We are to determine the justification by Anne to get the step 2 as shown

(4x^2 - 3) - 3 = -3(5x^2 - 2)

Expand

(4x^2 - 3) - 3 = -15x^2 + 6

Hence the justification used is multiplicative property of equality because both sides are multiplied by the same value

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A movie ends at 7:45 P.M. The next movie begins 50 minutes later. What time does the next movie begin?

Answers

Answer:

8:35 PM

Step-by-step explanation:

First, subtract 15 from 50.

50-15=35

Add that 15 taken from 50 to 7:45.

7:45 + 0:15 = 8:00

Add 35 to 8:00

8:00 + 0:35 = 8:35

The next movie will start at 8:35 PM.

Hope this helps!

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