a) The third moment of Z is zero. b) E[X] = μ + σ^2μ/3.
(a) To find the third moment of Z, we need to calculate E(Z^3):
Using the formula for the moment generating function of a standard normal distribution:
M(t) = E(e^(tZ)) = exp(t^2/2)
We can differentiate the moment generating function three times to get the third moment:
M''(t) = E(Z^2 e^(tZ)) = (t^2 + 1) exp(t^2/2)
M'''(t) = E(Z^3 e^(tZ)) = (t^3 + 3t) exp(t^2/2)
Therefore, E(Z^3) = M'''(0) = 0 + 3(0) = 0
So, the third moment of Z is zero.
(b) To find E(X), we can use the fact that X = μ + σZ.
Expanding the cube of X - μ in terms of Z, we get:
(X - μ)^3 = (σZ)^3 + 3(σZ)^2 (X - μ) + 3σZ(X - μ)^2 + (X - μ)^3
Taking the expectation of both sides and using linearity of expectation, we get:
E[(X - μ)^3] = E[(σZ)^3] + 3σE[(σZ)^2]E[X - μ] + 3σE[Z](E[X^2] - 2μE[X] + μ^2) + E[(X - μ)^3]
Since Z is a standard normal variable with mean 0 and variance 1, we have:
E[(σZ)^3] = σ^3 E[Z^3] = 0 (from part (a))
E[(σZ)^2] = σ^2 E[Z^2] = σ^2
E[Z] = 0
Also, we know that X is a normal random variable with mean μ and variance σ^2, so:
E[X] = μ
And,
E[X^2] = Var(X) + E[X]^2 = σ^2 + μ^2
Substituting these values into the equation above, we get:
E[(X - μ)^3] = 3σ^2μ + E[(X - μ)^3]
Solving for E[X], we get:
E[X] = μ + σ^2μ/3
Therefore, E[X] = μ + σ^2μ/3.
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GUYS PLEASE ANSWER THIS QUESTION BELOW. I AM 1 BRAINLIEST AWAY FROM EXPERT AND NEED SOMEONE ELSE TO ANSWER THIS QUESTION SO I CAN GET BRAINLIEST! YOU DON'T NEED TO ANSWER IT RIGHT JUST TYPE SOMETHING RANDOM!! Thank you!!
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Answer:
Done :)
Step-by-step explanation:
Best of luck!
Hey I'm Chloe Lol, Can You Help Me Thank you :)
Solve The following For x :
3( 3x+9) = 4(4 x+5)
3x-9=4
Step-by-step explanation:
Answer:
x = 1
Step-by-step explanation:
3(3x+9)=4(4x+5) distribute through multiplication
9x + 27= 16x + 20 subtract 9x and 20 from both sides
7 = 7x divide both sides by 7
x =1
check work
3(3(1)+9) = 4(4(1)+5) distribute the x
3(12) = 4(9)
36 = 36
Congrats I hope this helped!
12 parents volunteered to
chaperone the dance. If 15% of all
parents polled volunteered, how
many parents were asked to
volunteer?
Answer:
80
Step-by-step explanation:
15/100x=12
3/20x=12
x=12*20/3=80
if my answer helped please mark as brainliest.
Answer:
if 15% of all parents polled volunteered, then 80 parents were asked to volunteer.
Step-by-step explanation:
Okay so basically 12 is 15% of a number therefore 12/? = 15%/100?
So we multiply 12 x 100= 1200
Then divide 1200 ÷ 15 to get your answer.
1200 ÷ 15 = 80
Ella is 66 inches tall. Andy is 6 1/2 feet tall. Who is taller? By how much? (12 inches = 1 foot)
Answer:
Andy is taller by one foot or 12 inches
Step-by-step explanation:
Ella = 66 inches = 5'6"
Andy = 6 1/2 feet = 6'6"
Andy is taller by one foot or 12 inches
Andy is taller by one foot or 12 inches
Given:
Ella is 66 inches and Andy is 6 1/2 feet.
12 inches = 1 feet.
Convert inches in to feet.
12 inches = 1 feet.
1 inches = 1/12 = 0.083
66 inches = (0.083 * 66) = 5.5 feet.
Andy = 6 1/2 feet = 6.5 feet.
6.5 > 5.5 (6.5 is greater than 5.5).
Andy is taller by one feet or 12 inches
Therefore, Andy is taller by one feet.
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Find the solution of the equation. 2(2x + 3) = -4 + 2(2x + 5)
Answer:
x = 2/3
Step-by-step explanation:
4x + 6 = 10x + 10
4x = 10x - 4
6x - 4
x = 2/3
Have a great day <3
Quadrilateral ABCD has side lengths of 2, 5, 7, and 12. A
new quadrilateral is created, using a scale factor of 0.25.
Which of the following are side lengths of the new
quadrilateral?
Quick first gets brainliest!!
Answer:
You didnt put any answer choices but by applying that scale factor, I got these measurements in the order you put them in. 0.5. 1.25. 1.75. 3.
Plsssss help me, It says find the area
Answer:
It should be 136
Step-by-step explanation: I split it up into multiple pieces
Rectangle 1= 20*2=40
Rectangle 2= 14*4=56
Rectangle 3= 20*2=40
40+40+56=136
Use a unit multiplier to convert 0.37 liters to milliliters.
Answer:
370
Step-by-step explanation:
Multiply the number of liters (L) by 1,000 to find the number of milliliters (mL). There are 1,000 times as many milliliters as there are liters. For instance, say you have 3 liters. Simply multiply 3 liters by 1,000 to get 3,000 milliliters.
Find the x- and y-intercepts of the graph of x + 5y = 6 state your answer as whole numbers or as improper fractions in simplest form
Answer:
[tex]y=-\frac{1}{5}x+\frac{6}{5}[/tex]
Step-by-step explanation:
Let's solve for x.
[tex]x+5y=6[/tex]
Step 1: Add -5y to both sides.
[tex]x+5y+-5y=6+-5y[/tex]
[tex]x=-5y+6[/tex]
Answer:
[tex]x=-5y+6[/tex]
Let's solve for y.
[tex]x+5y=6[/tex]
Step 1: Add -x to both sides.
[tex]x+5y+-x=6+-x[/tex]
[tex]5y=-x+6[/tex]
Step 2: Divide both sides by 5.
[tex]\frac{5y}{5}=\frac{-x+6}{5}[/tex]
[tex]y=\frac{-1}{5} x+\frac{6}{5}[/tex]
Answer:
[tex]y=\frac{-1}{5} x+\frac{6}{5}[/tex]
the equati...
Solve the equation 3(x + 4.5) = 36.
If you get stuck, use the diagram.
36
4.5
X = ?
Answer:
x = 7.5
Step-by-step explanation:
Answer:
75
Step-by-step explanation:
if you put 3 in the x it is now 3 but the x it is there with the 3 and do 3 with the 4.5 and then add them to each of them then you get your answer
can some one help me please....
by step by step explanation......
Help me please answer all thanks
Answer:
the coordinates are (3,3)
Step-by-step explanation:
hope I helped!!
If it costs $300 to tile a 420 square foot room, how much will it cost to tile a
room with 1,050 square feet?
Answer:
750$
Step-by-step explanation:
[tex]Amount= 300*\frac{1050}{420} =750[/tex]
It will cost approximately $750.01 to tile a room with an area of 1,050 square feet.
To find out how much it will cost to tile a room with 1,050 square feet, we can set up a proportion using the given information.
Cost₁: The cost to tile the first room with an area of 420 square feet, which is $300.
Area₁: The area of the first room, which is 420 square feet.
Cost₂: The cost to tile the second room with an unknown area, which we want to find.
Area₂: The area of the second room, which is 1,050 square feet.
We can set up the proportion:
Cost₁ / Area₁ = Cost₂ / Area₂
Substituting the known values:
$300 / 420 sq ft = Cost₂ / 1,050 sq ft
Now we can solve for Cost₂:
Cost₂ = ($300 / 420 sq ft) * 1,050 sq ft
Calculating:
Cost₂ = $0.7143 * 1,050 sq ft
Cost₂ ≈ $750.01
Therefore, it will cost approximately $750.01 to tile a room with an area of 1,050 square feet.
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helppppp pleaaaaaseee
someone on this god forsaken planet help me
Answer: Lol
B (-8,-5)
D (-10,-4)
C (-8,3)
Step-by-step explanation:
Simplify
(2m-m) - (3m+4n)
The population of a city has increased by 38% since it was last measured. If the current population is 89,700, what was the previous population.
Answer:
65000
Step-by-step explanation:
Given data
Let the previous population be x
the increase was by 38%
The expression below describes the current population
38/100*x+ x=89700
0.38x+x= 89700
1.38x= 89700
x= 89700/1.38
x= 65000
Hence the previous population is 65000
what is the sum of 3aa+5aa=
Answer:
8aa
Step-by-step explanation:
Answer:
8aa is the correct answer of this question
define el concepto de renacimiento y el de humanismo
Answer:
Renacimiento es el nombre dado en el siglo XIX a un amplio movimiento cultural que se produjo en Europa Occidental durante los siglos XV y XVI. ... El Renacimiento fue fruto de la difusión de las ideas del humanismo, que determinaron una nueva concepción del hombre y del mundo.
Step-by-step explanation:
Please give thanks to all my answers and please mark as brilliant and please follow me
i need helpppppppppppppp
Answer:
B
Step-by-step explanation:
Factor out 1/4.
1/4 - 3/4 x = (1/4)(1 - 3x)
Answer: B
Help PLEASE I forgot how to do this :'(
Answer:
C) The sum of the first 2 terms after the fourth term.
The table represents some points on the graph of the exponential function that models the radioactive decay of a sample of xenon-135.
Which statement about the graph of this function is true?
(See the picture below)
A) There is an asymptote at y = 70.
B) The y-intercept is located at (0, 70).
C) There is an asymptote at x = 0.
D) The x-intercept is located at (70, 0).
Answer: b the y-intercept is located at (0,70)
The exponential curve passes through the point (0, 70). Then the correct option is B.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
The table addresses a few focuses on the diagram of the outstanding capability that models the radioactive rot of an example of xenon-135.
At x = 4.6, the value of 'y' will be 49.5.
[tex]\rm 49.5 = ab^{4.6} \ \ \ \ \ \ \ ...1\\[/tex]
At x = 9.2, the value of 'y' will be 35.
[tex]\rm 35= ab^{9.2} \ \ \ \ \ \ \ ...2[/tex]
From equations 1 and 2, then we have
[tex]\rm \dfrac{b^{9.2}}{b^{4.6}} = \dfrac{35}{49.5}\\\\b^{4.6} = 0.707\\\\b = 0.927\\[/tex]
Then the value of 'a' will be
[tex]\rm 49.5 = a (0.927)^{4.6}\\\\a = 70[/tex]
Then the equation is given as,
y = 70 · (0.927)ˣ
The graph is given below.
The exponential curve passes through the point (0, 70). Then the correct option is B.
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What is the solution to the equation?
Answer:
C. x = 63
Step-by-step explanation:
X ÷ 3 = 21 is the same as 3 × 21 which is 63.
PLEASE ANSWER ASAP!
Find (f+g)(x).
f(x) = 1/x
g(x) = x² + 2x - 5
-----------------------
a.) 1/x - x² - 2x b.) 1/x + x² + 2x - 5
c.) x² + 2x -5 - 1/x d.) 1/x + x² - 5
Answer:
I think it is b but I could be wrong
2) Solve the System of Equations using Substitution.
-3x+2y=12
x=2y-8
Answer:
x=-2. y=3
Step-by-step explanation:
So, it tells us that x=2y-8.
Now substitute x into the equation.
-3(2y-8)+2y=12
- 6y+24+2y=12
-4y+24=12
-4y=-12
y=-12/-4
y=3
Now that we know that y=3 substitute y into the second equation equation.
x=2(3)-8
x=6-8
x=-2
So in the end x=-2 and y=3
Hope this helps
Answer:
y=3, and x= -2
Step-by-step explanation:
-3x= -2y+12
x=2y-8
3x=2y-12
3x=6y-24
2y-12=6y-24
-4y=-12
y=3
x= -2
Michael sells 136 newspapers each week. If there are 52 weeks in a year, how many newspapers does Michael sell in a year?
Answer:
7,072
Step-by-step explanation:
136 times 52 = 7,072
Answer:
7,072 newspaper in a year
Step-by-step explanation:
Multiply: 136*52=7,072
(I would put a picture of my work but I'm lazy right now lol)
Hope this helped!! :)
Stay safe and have a wonderful day/night!!!!!
Brainliest?!?!
Evaluate the expression when when c = 3 and d = 33
Answer:
45
Step-by-step explanation:
Plzz write with formula and explanation plzzzzzzzz answer fast
Answer:
Rs 19 1/8
Step-by-step explanation:
Fromm the above question, we are told that:
The cost of 2/3 meters of rope = Rs 12 3/4
We are asked to calculate the cost per meter of rope.
Hence:
2/3 meters of rope = Rs 12 3/4
1 meter of rope = Rs x
Cross Multiply
2/3x = 1 × 12 3/4
x = 12 3/4 ÷ 2/3
x = 51/4 ÷ 2/3
x = 51/4 × 3/2
x = 153/8
x = Rs 19 1/8
Therefore, the Cost per meter of rope = Rs 19 1/8
what is the square root of 169
Answer: 13
Step-by-step explanation:
NEE HELP!
Solve for x, round your answer to the nearest hundredth: 5lnx + 2 = 17
*need step-by-step solution
Answer:
e^3
Step-by-step explanation:
5ln(x)+2=17
5ln(x)=17-2
5ln(x)=15
ln(x)=15/5
ln(x)=3
e^ln(x)=e^3
x=e^3