Suppose X ~ Bernoulli(p), such that P(X=1)=p. Find the following. a. Find E[e-2X] b. Find Var(e-2X)...

Suppose X ~ Bernoulli(p), such that P(X=1)=p. Find the following.

a. Find E[e-2X]
b. Find Var(e-2X)
c. Find E[6 – 4X2]
d. Find Var(6 – 4X2)

Solutions

Expert Solution

a) The expected value here is computed as:

This is the required expected value here.

b) The second moment of e-2x is computed here as:

Therefore the variance of e-2x is computed here as:

This is the required variance here.

c) The expected value here is computed as:

This is the required expected value here.

d) The variance here is computed as:

This is the required variance here.

orchestra answered 1 year ago

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