Consider the following joint distribution 10.1 0.3 20.4 0.2 Define W-X2 Y? (a) F

Question

Consider the following joint distribution 10.1 0.3 20.4 0.2 Define W-X2 Y? (a) Find E(W) using the equation where x,-1,T2 = 2, y,-1,U2-2 with column headings W and p(W) formula for the expected value (b) Find p(W), that is find the marginal distribution of W. Give your answer as a table (c) Check you answer to part (a) using the distribution you found in part (b) and the where w,... , we is the support (possible values) of W No answer is required for this question. I just want to show you the two different ways to find E(W)

Explanation / Answer

(a)

E(W)=(12+12)*0.1+(12+22)*0.3+(22+12)*0.4+(22+22)*0.2=0.2+1.5+2.0+1.6=5.3

(b)

(c)

E(W)=2*0.1+5*0.7+8*0.2=0.2+3.5+1.6=5.3

w 2 (when x=1,y=1) 5 (x=1,y=2 and x=2,y=1) 8 (x=2,y=2) P(W=w) 0.1 0.7 (P(x=1,y=2)+P(x=2,y=1)) 0.2

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