SOLUTION: You are told that E(X)=8 and var(X)=4. What are the expected values and variances of the following expressions: a. Y= 3X-2 b. Y= 0.6X-4 c. Y= X/4 d. Y= aX+b, where a and b ar

Question 394836: You are told that E(X)=8 and var(X)=4. What are the expected values and variances of the following expressions:
a. Y= 3X-2
b. Y= 0.6X-4
c. Y= X/4
d. Y= aX+b, where a and b are constants
e. Y= 3X^2+2
Found 2 solutions by stanbon, robertb:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
You are told that E(X)=8 and var(X)=4.
What are the expected values and variances of the following expressions:
a. Y= 3X-2
E(3X-2) = 3E(X)-2 = 3*8-2 = 22
Var(3X-2) = (3)^2*Var(X) = 9*4 = 36
----------------------------------
b. Y= 0.6X-4
E(0.6X-4) = 0.6*E(X)-4 = 0.6*8-4 = 0.8
Var(0.6X-4) = (0.6)^2*Var(X) = 0.36*4 = 1.44
--------------------
c. Y= X/4
E((1/4)X) = (1/4)E(X) = 2
Var((1/4)X) = (1/4)^2*Var(X) = 4/16 = 1/4
-------------------------
d. Y= aX+b, where a and b are constants
E(aX+b) = aE(x)+b = 8a+b
Var(aX+b) = a^2*Var(X) = 4a^2
----------
e. Y= 3X^2+2
E(3X^2+2) = 3*E(X^2)+2
Var(3X^2+2) = 9*E(X^2)
=============================
Cheers,
Stan H.

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
e.

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Now

=
=.
Hence .
is the 4th moment about the origin, and can't be evaluated without knowledge of the density function.
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