A box contains four tags numbered -2,2 tags numbered 0, 1tag numbered 1 and 3 ta
ID: 2913827 • Letter: A
Question
A box contains four tags numbered -2,2 tags numbered 0, 1tag numbered 1 and 3 tags numbered 2. A tag is selected at randomfrom the box. Let W denote the number on the tag. Compute: 1) E(W) 2) Var(W) 3) E(2W+15) 4) Var(-2W) 5) Var(3W+21)If W is a random variable given in the previous problem,compute P([W is greather than or equal to two]), P([W is greaterthan or equal to zero]) and P[W is greater than or equal toone]). A box contains four tags numbered -2,2 tags numbered 0, 1tag numbered 1 and 3 tags numbered 2. A tag is selected at randomfrom the box. Let W denote the number on the tag. Compute: 1) E(W) 2) Var(W) 3) E(2W+15) 4) Var(-2W) 5) Var(3W+21)
If W is a random variable given in the previous problem,compute P([W is greather than or equal to two]), P([W is greaterthan or equal to zero]) and P[W is greater than or equal toone]).
Explanation / Answer
W -2 -2 -2 -2 0 0 1 2 2 2 p(x)1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1) E(W) =-2(1/10)-2(1/10)-2(1/10)-2(1/10)+0(1/10)+0(1/10)+2(1/10)+2(1/10)+2(1/10) =-8/10+0+6/10 = -2/10 = -1/5 2) V(W) =4*(1/10)+ 4*(1/10)+ 4*(1/10)+ 4*(1/10)+ 0*(1/10)+ 0*(1/10)+ 4*(1/10)+ 4*(1/10)+ 4*(1/10)- (-1/5)2 = 28/10 - (1/25) =14/5-(1/25) = (70-1)/25 =69/25 3)E(2W+15) = 2E(W)+15 =2(-1/10)+15 4) V(-2W) = 4V(W) = 4*(69/25) 5)V(3W+21) = 9V(W) =9(69/25)Related Questions
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