Question

I'm trying to solve this problem:

Let Y ~ Bin (8, 0.5)

Find E(7^Y - 36Y² + 8Y -4)

I know how to simplify all the terms except for E(7^Y), so what I have so far is: E(7^Y) - 36V(Y) + 8E(Y) - 4. How do I simplify E(7^Y) so that I can solve the problem?

Answer 1

How do I simplify E(7Y) so that I can solve the problem?

This is your question.

E(7Y) = 7*E(Y)

Let Y ~ Bin (8, 0.5)

n = 8

p = 0.5

We know that E(Y) = n*p = 8*0.5 = 4

V(Y) = n*p*(1-p) = 8*0.5*0.5 = 2

E(7Y) = 7*E(Y) = 7*4 = 28

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Lets solve all question in detail.

We have to find E(7Y - 36+ 8Y -4)

n = 8

p = 0.5

We know that E(Y) = n*p = 8*0.5 = 4

V(Y) = n*p*(1-p) = 8*0.5*0.5 = 2

E(7Y - 36+ 8Y -4) = 7*E(Y) - 36*E() + 8*E(Y) - 4

E(7Y - 36+ 8Y -4) =  7*E(Y) - 36*( V(Y) + (E(Y))^2) + 8*E(Y) - 4

E(7Y - 36+ 8Y -4) = 7*4 - 36*( 2 + 16) + 8*4 - 4 = 28 - 648 + 32 - 4 = - 592