A box contains four tags numbered -2,2 tags numbered 0, 1tag numbered 1 and 3 ta

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)                       

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