Proceed with the assumptions from Problem 5. A continuous random variableQhas cumulative distribu- tion function

FQ(q)=4q33q4for (0q1) andFQ(q) = 0 forq <0,whileFQ(q) = 1 forq >1.

GivenQ=q,an integer-valued random variableNhas probability mass function:

for (0n2)

P[N=n|Q=q]=

1. Evaluateconditionaldensity of (Q|N=n) for all values ofN.

fQ|N(q|0) =fQ|N(q|1) =fQ|N(q|2) =

2!n2n

n!(2n)!

q(1q)

2. Determineconditionalexpectation ofQ,givenN=nfor valuesn= 0, n= 1,andn= 2.E[Q|N= 0] =

E[Q|N= 1] =E[Q|N= 2] =