## Question

###### QUESTION 12Let 0 = {a,b,C,d,e} ad let P be a probability measure on 0 such that P({a})= .2,P({b})= 3,P({c})= .1,P({d}) 25,P({e}) .15. Define the sigma-algebra $ as follows: F ={@,{a,b,c} {a,c,d,e}{a,c} 0,{b,d,e} {b} {d,e}} For the random variable X given by X(a)=X(b)= 2X(c)=X(d)=1,X(e)=3,compute E(X | F) and evaluate this random variaole at W=e.0 2 1.80 70 None ofthe alternatives is correct: 5

QUESTION 12 Let 0 = {a,b,C,d,e} ad let P be a probability measure on 0 such that P({a})= .2,P({b})= 3,P({c})= .1,P({d}) 25,P({e}) .15. Define the sigma-algebra $ as follows: F ={@,{a,b,c} {a,c,d,e}{a,c} 0,{b,d,e} {b} {d,e}} For the random variable X given by X(a)=X(b)= 2X(c)=X(d)=1,X(e)=3,compute E(X | F) and evaluate this random variaole at W=e. 0 2 1.8 0 7 0 None ofthe alternatives is correct: 5

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