1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
solong [7]
3 years ago
5

Let $\mu$ and $\sigma^2$ denote the mean and variance of the random variable x. determine $e[(x-\mu)/\sigma]$ and $e{[((x-\mu)/\

sigma)^2]}$
Mathematics
1 answer:
Nezavi [6.7K]3 years ago
3 0
\mathbb E\left(\dfrac{X-\mu}{\sigma}\right)=\dfrac1\sigma\mathbb E(X)-\dfrac\mu\sigma=\dfrac{\mu-\mu}\sigma=0

\mathbb E\bigg(\left(\dfrac{X-\mu}\sigma\right)^2\bigg)=\dfrac1{\sigma^2}\mathbb E\left(X^2-2\mu X+\mu^2\right)=\dfrac{\mathbb E(X^2)-2\mu\mathbb E(X)+\mu^2}{\sigma^2}
=\dfrac{\mathbb E(X^2)-2\mu^2+\mu^2}{\sigma^2}=\dfrac{\mathbb E(X^2)-\mu^2}{\sigma^2}=\dfrac{\mathbb E(X^2)-\mathbb E(X)^2}{\sigma^2}
=\dfrac{\mathbb V(X)}{\sigma^2}=\dfrac{\sigma^2}{\sigma^2}=1
You might be interested in
draw a model to represent the problem. 2/3 divided into 1/3 size pieces. how many 1/3 pieces will be in 2/3?
Hunter-Best [27]
That shows the answer of how to do it 

6 0
3 years ago
For his birthday party Jacob mixed together 8 gal. Of Brand A fruit punch and 2 gal. of brand B. Brand A contains 60% fruit juic
REY [17]
The answer is 5 gallons
Its very simple. 
Turn 60% and 10% into decimals ( .60 and .10)
Multiply 8 gallons ( brand A ) by .60 and you get 4.8 gallons
Multiply 2 gallons ( brand B ) by .10 and you get .2 gallons
Add them up and you get 5 gallons.

3 0
3 years ago
The European power to first gain a foothold in India was ___________ .
Shkiper50 [21]
D is the answer :) lol
8 0
2 years ago
Read 2 more answers
Which mathematical sentence is represented by the diagram
ElenaW [278]

Answer:

I will attach a picture, but I need you to attach a screenshot so I can solve it.

Step-by-step explanation:

But here:

7 0
2 years ago
Fernando has some nickels, dimes, and quarters that are worth a total of $3.25. He has twice as many dimes as nickels. He has 3
CaHeK987 [17]

Answer:

Number of nickels = 5

Number of dimes = 10

Number of quarters = 8

Step-by-step explanation:

Fernando has a total of nickels + dimes + quarters = 3.25$

Let the number of nickels = x

Then x(.05) + dimes(.10) + quarters(0.25) = 3.25------(1)

He has twice as many dimes as nickels

dimes = 2×nickels

dimes = 2x--------(2)

He has 3 more quarters than nickels

quarters = nickels +3

quarters = x +3------(3)

From equations 1, 2, and 3.

x(.05) + 2x(.10) + (x + 3)(.25) = 3.25

.05x + 0.2x + 0.25x + .75 = 3.25

5x + 20x + 25x + 75 = 325

50x = 325 - 75

50x = 250

x = 5

Therefore the number of nickels are 5

from equation 2 number of dimes are 10

and from equation 3 number of quarters are 8.

3 0
3 years ago
Other questions:
  • Find the complete factored form of the<br> polynomial:<br> -24a^4 – 20a^3
    10·1 answer
  • 1. A 2012 survey conducted by the local paper in Columbus, Ohio one week before Election Day
    15·1 answer
  • How many inches in a full step?
    14·2 answers
  • Please help, it's due today<br><br>thank you :D​
    13·1 answer
  • How do I solve this math problem?
    6·1 answer
  • Guess the number.The number has two digits. The sum of the digits is eight. If the digits are reversed, the results is 18 less t
    15·1 answer
  • What is the midline equation of y = 2 sin( pi/2 x+3)?​
    10·1 answer
  • Find the Missing angle <br>​
    10·2 answers
  • Create interview questions.<br> Conduct three interviews.<br> Answer them. Brainliest!
    9·1 answer
  • If y varies inversely to x and y=9 when x=-6 find x when y=3
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!