The CDF of Y evaluated at y = 0.72 is 0.1296.
Since X1 and X2 are independent and uniformly distributed over [0, 2], their joint density function is:
f(x1, x2) = 1/4, for 0 ≤ x1 ≤ 2 and 0 ≤ x2 ≤ 2
To find the CDF of Y, we can use the fact that:
Fy(y) = P(Y ≤ y) = P(max(X1, X2) ≤ y)
This event can be split into two cases:
X1 and X2 are both less than or equal to y:
In this case, Y will be less than or equal to y.
The probability of this occurring can be calculated using the joint density function:
P(X1 ≤ y, X2 ≤ y) = ∫0y ∫0y f(x1, x2) dx1 dx2
= ∫0y ∫0y 1/4 dx1 dx2
[tex]= (y/2)^2[/tex]
[tex]= y^2/4[/tex]
One of X1 or X2 is greater than y:
In this case, Y will be equal to the maximum of X1 and X2.
The probability of this occurring can be calculated as the complement of the probability that both X1 and X2 are less than or equal to y:
P(X1 > y or X2 > y) = 1 - P(X1 ≤ y, X2 ≤ y)
[tex]= 1 - y^2/4[/tex]
Therefore, the CDF of Y is:
Fy(y) = P(Y ≤ y) = P(max(X1, X2) ≤ y)
= P(X1 ≤ y, X2 ≤ y) + P(X1 > y or X2 > y)
[tex]= y^2/4 + 1 - y^2/4[/tex]
= 1, for y ≥ 2
[tex]= y^2/4,[/tex]for 0 ≤ y ≤ 2
To find Fy(0.72), we simply substitute y = 0.72 into the expression for Fy(y):
[tex]Fy(0.72) = (0.72)^2/4 = 0.1296[/tex]
For similar question on probability.
https://brainly.com/question/30403935
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Since X1 and X2 are uniformly distributed over [0, 2], their probability density functions (PDFs) are:
fX1(x) = fX2(x) = 1/2, for 0 <= x <= 2
To find the CDF of Y = max(X1, X2), we need to consider two cases:
1. If y <= 0, then Fy(y) = P(Y <= y) = 0
2. If 0 < y <= 2, then Fy(y) = P(Y <= y) = P(max(X1, X2) <= y)
We can find this probability by considering the complementary event, i.e., the probability that both X1 and X2 are less than or equal to y. Since X1 and X2 are independent, this probability is:
P(X1 <= y, X2 <= y) = P(X1 <= y) * P(X2 <= y) = (y/2) * (y/2) = y^2/4
Therefore, the CDF of Y is:
Fy(y) = P(Y <= y) =
0, y <= 0
y^2/4, 0 < y <= 2
1, y > 2
To find Fy(0.72), we substitute y = 0.72 into the CDF:
Fy(0.72) = 0.72^2/4 = 0.1296
Therefore, the value of Fy(y) at y = 0.72 is 0.1296.
Learn more about cumulative distribution function (CDF) here: brainly.com/question/31961014
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Need help ASAP I will give you 10 points
Answer: x=18
Step-by-step explanation:
First distribute:
(18/6)-(x/6)=0
Isolate the x variable:
(18/6)=(x/6)
18=x
PLS HELP 30 PTS!!!Use the coordinate plane to help you identify the length of each leg then use the Pythagorean Theorem to find the length of CD
Type your answer in the box.
Note: Type in only numeric part of the answer. Round your answer to the nearest hundredth.
Example: 12.70
Answer:
it says 15 points not 30
Step-by-step explanation:
Answer:
10.30
Step-by-step explanation:
Pythagorean Theorem is [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]. The short leg(a) is 5 units long and the long leg(b) is 9 units long. CD is the hypotenuse, the longest side (c).
[tex]5^{2}[/tex] +[tex]9^{2}[/tex] =[tex]c^{2}[/tex]
25+81=[tex]c^{2}[/tex]
106=[tex]c^{2}[/tex]
[tex]\sqrt{106}[/tex] = [tex]\sqrt{c^{2} }[/tex]
10.29563014 = c
Rounded to the nearest hundredth, 10.30
To check this is correct, the hypotenuse is the longest side, and 10.30 is longer than 5 and 9.
what is the circumfrence of this circle? pi=3.14 formulas: C = (pi) * d (or) c=2*(pi) * r
Answer:
75.36 cm
Step-by-step explanation:
Given.
radius (r) = 12 cm
Circumference (C)
= 2*π*r
= 2 * 3.14 * 12
= 75.36 cm
Hope it will help :)
solve the equation r4·r3 = _____
Jonathan says that when you add 7 2 3 to 2 2 3 , you must add the whole numbers together first ( 7 + 2 = 9 ). Then you just add the numerators together ( 2 + 2 = 4 ), and you add the denominators together ( 3 + 3 = 6 ). So the answer is 9 4 6 . Unfortunately, Jonathan's strategy is incorrect. Solve this problem, and then briefly explain the flaw in Jonathan's reasoning.
Answer:
9 4/3
Step-by-step explanation:
Jonathan working:
Add 7 2/3 to 2 2/3
Step 1: you must add the whole numbers together first ( 7 + 2 = 9 ).
Step 2: Then you just add the numerators together ( 2 + 2 = 4 ),
Step 3: you add the denominators together ( 3 + 3 = 6 ).
Step 4: Answer is 9 4/6
Correct workings:
Add 7 2/3 to 2 2/3
Step 1: you must add the whole numbers together first ( 7 + 2 = 9 ).
Step 2: Then you just add the numerators together ( 2 + 2 = 4 ),
Step 3: you pick one of the denominators because they are the same (3)
Step 4: Answer is 9 4/3
Which point has the coordinates (2, 3)?
у
5
4
B.
С
3
2
D
A
1
0
1
2
з
4
х
5
ОА
ОС
OD
ОВ
Answer:
Point B
Step-by-step explanation:
The first number in the brackets is X while the second is Y (x, y).
X is the bottom line, while Y is the line going up.
Find 2 on the bottom line and 3 on the upright line. This gives us B.
I am sorry for the poor explanation.
The perimeter of a square is represented by the expression 32x-12. . Write two equivalent expressions for the perimeter and explain how to find the length of one side. x=3
Answer:
P = 2(l+w) ----------(1)
P = 4l----------- (2)
P= 32x- 12
4l = 32x- 12
l = 8x- 3
One side will be equal to 21 units and the perimeter will be 84 units when x=3.
Step-by-step explanation:
The perimeter is given by the formula
P = 2(l+w) ----------(1)
where p= perimeter , l= length and w= width.
But a square has the length equal to the width so w= l and the formula becomes
P = 2( l+l)
P = 2 (2l)
P = 4l----------- (2)
The perimeter of the square is
P= 32x- 12
or
4l = 32x- 12
dividing the whole equation by 4 we get
l = 8x- 3
So the length of one side can be obtained by dividing the perimeter by 4.
If x= 3
then
l= 8(3)-3
l= 24- 3
l = 21
One side will be equal to 21 units and the perimeter will be 84 units.
P = 4l = 4(21)= 84
20000 students took a standardized math test. The scores on the test are normally distributed, with a mean score of 85 and a standard deviation of 5. About how many students scored between 90 and 95?
Answer: 2718
Step-by-step explanation:
Given: Mean score = 85
Standard deviation = 5
Let x be the score of a random student that follows normal distribution.
Then, the probability that a student scored between 90 and 95 will be
[tex]P(90< x < 95)\\\\=P(\dfrac{90-85}{5}<\dfrac{x-\mu}{\sigma}<\dfrac{95-85}{5})\\\\= P(1< z< 2)\ \ \ \ \ [z=\dfrac{x-\mu}{\sigma}]\\\\=P(z<2)-P(z<1)\\\\=0.9772-0.8413\\\\=0.1359[/tex]
The number of students scored between 90 and 95 = 0.1359 x (Total students)
= 0.1359 (20000)
= 2718
Hence, The number of students scored between 90 and 95 = 2718
Find the value of 9x-5 given that – 2x-3=5.
Simplify your answer as much as possible.
Answer:
The value of 9x - 5 is -41.
Step-by-step explanation:
-2x - 3 = 5
-2x = 5 + 3
-2x = 8
x = -4
9x - 5
= 9(-4) - 5
= -36 - 5
= -41
Suppose the radius of a circle is three units what is the circumference
Answer:
[tex]6\pi[/tex] or [tex]18.84[/tex] units
Step-by-step explanation:
The circumference of a circle can be found using the formula [tex]C=2\pi r[/tex], where [tex]C[/tex] is the circle's circumference and [tex]r[/tex] is the circle's radius. We know that [tex]r=3[/tex] and that we are solving for [tex]C[/tex]. Therefore:
[tex]C=2\pi r\\C=2*\pi *3\\C=6\pi[/tex]
Since [tex]\pi[/tex] is approximately [tex]3.14[/tex], [tex]6\pi =6*3.14=18.84[/tex] units. Hope this helps!
Use the Distributive Property to rewrite the algebraic expression. 5(2x + 7)
wrong answers reported, correct answers get 5 stars
Answer:
10x + 35
Step-by-step explanation:
In distributive property, you have to distribute that 5 to both the 2x and the 7, so then it would look like this:
5(2x) + 7(5)
Then we just further simplify and get:
10x + 35.
Hope this helped, let me know if you have any questions
What is greater 100,000 cm or 1 mi PLEASE HELPPPPPPP
Answer:
1 mile
Step-by-step explanation:
1m =160934 cm
A circular cylinder has a curved surface area 1320cm square and the radius of its base is 10.5cm find the height and volume of cylinder.
Answer:
h=9.51
v=3293.89
Step-by-step explanation:
hope it helps :)
Answer:
h = 9.51
v = 3293.89
Step-by-step explanation:
please mark me as brainliest
find the tangents of the acute angle in the right triangle. write each answer as a fraction
Answer:
[tex]tanD=\frac{7}{24}[/tex]
[tex]tanF=\frac{24}{7}[/tex]
Step-by-step explanation:
We are given that
ED=24units
EF=7units
FD=25 units
We have to find the tangents of the acute angle in the right triangle
We know that
tangent=[tex]\frac{Perpendicular\;side}{Base}[/tex]
Using the formula
[tex]tanD=\frac{EF}{ED}[/tex]
[tex]tanD=\frac{7}{24}[/tex]
[tex]tanF=\frac{ED}{EF}[/tex]
[tex]tanF=\frac{24}{7}[/tex]
find the fourth proportional to 2,3,6
Answer:
9
Step-by-step explanation:
Let the fourth proportional be x Then
2 : 3 :: 6 : x
2/3 = 6 / x
2x = 3 * 6
x = 18 / 2
x = 9
Hope it will help :)
what is the mean of the data set? 16, 24, 26, 13
Answer:
20
Step-by-step explanation:
17+24+26+13=80
80/4=20
I need help with this question.
Answer:
[tex]13 {z}^{8} [/tex]
Step-by-step explanation:
-2(3x-4)+3x=17 solve for x
Answer:
The answer will be -3
Step-by-step explanation:
Hope this Helped
Answer:
x= -3
Step-by-step explanation:
It is really Easy just Isolate the variable by dividing each factor that don't contain the variable
Over the course of 3 days, Calvin spent 10 hours delivering newspapers. He spent the same amount of time each day delivering newspapers. Which of the following equations represents the amount of time Calvin spent delivering papers each day?
A: 3 ÷ 10
B: 10 ÷ 3 =
C:10 ÷ 7 =
D: 7 ÷ 10 =
The Flightless Folly ship has 20 pirates aboard. 12 of those pirates wear an eye patch. What percentage of pirates wear an eye patch on the Flightless Folly?
Write an equation and solve: At Trader Joes, Mrs.
Jacobs buys bananas for $0.65 per pound and a
frozen pizza for $4.99. The total for her purchase
was $6.94. How many pounds of bananas did
Mrs. Jacobs buy?
Please I’m desperate and tell me how you did it
Given:
Triangle EFG is similar to triangle HIJ.
To find:
The measure of side IJ.
Solution:
We know that, corresponding sides of similar triangles are proportional.
Triangle EFG is similar to triangle HIJ.
[tex]\dfrac{EF}{HI}=\dfrac{FG}{IJ}[/tex]
Putting the given values, we get
[tex]\dfrac{7}{32}=\dfrac{4}{IJ}[/tex]
[tex]7\times IJ=4\times 32[/tex]
[tex]IJ=\dfrac{128}{7}[/tex]
[tex]IJ=18.2857[/tex]
[tex]IJ\approx =18.3[/tex]
Therefore, the measure of side IJ is 18.3 units.
Need help!!!!!! this is for a grade
On Monday ,bo saw 1/5 of birds listed in his guidebook. on Tuesday he saw 3/5 more of birds. what fraction of the birds in the guidebook did bo see in those two days ?
Answer:
4/5Step-by-step explanation:
That would be 1/5 + 3/5 which equals (1+3)/5 = 4/5
Mare has a monthly cell phone plan that has a fixed charge of $12 per month plus
$0.30 per text message. Marie wants to spend no more than $40 per month on her
call phone. Which inequality represents the number of text messages, X, that Marie
Please hurry
You need to multiply the cost per text message by the number of messages (x) add that to the fixed charge.
The total of those need to be less than or equal to the amount she wants to spend.
The equation would be written as:
0.30x + 12 <= 40
Is y=9 a horizontal line or vertical
Answer:
Horizontal
Step-by-step explanation:
Answer:
y = 9 is a horizontal line :)
Step-by-step explanation:
y=9 is the equation of a horizontal line. The slope is 0. This means that for any value of x that is chosen, the y-value is always 9 Hence y=9 .
expand the following: 4(2x + 1)
Answer:
the equivalent expression is 8x + 4
Step-by-step explanation:
4(2x + 1) = 4x2 = 8 =
8x + 1 = 4x1 = 4 =
8x + 4
To check your work substitute 1
4(2(1) + 1) = 4(2 + 1) = 4(3) = 12
8(1) + 4 = 8+4 = 12
therefore they are both equivalent
hope this helped!
What is the complete factorization of the polynomial below? x3 + x2 + 4x + 4
Answer:
(x+1)(x+2/)(x-2/)
Step-by-step explanation:
what 20,000 divided by 24 ?
Answer:
833.3333333
Step-by-step explanation:
hope this helps
Step-by-step explanation:
[tex]\qquad\sf\dashrightarrow 20000/24 [/tex]
[tex]\qquad\sf\dashrightarrow 10000/12 [/tex]
[tex]\qquad\sf\dashrightarrow 5000/6 [/tex]
[tex]\qquad\sf\dashrightarrow 2500/3 [/tex]
[tex]\qquad\sf\dashrightarrow 833.3 [/tex]
Someone plz help me I wil give brainliest
Answer:
The answer is three quarters, one nickel's dime, and a penny!
Step-by-step explanation:
Answer:
Dime- 4
Penny- 1
Half Dollar- 1
Step-by-step explanation:
A dollar is 100 cents and you have 91
91- 50 (half dollar)= 41
41- 1 (one penny)= 40
40- 40 (4 dimes)= 0