The pmf of the amount of memory X (GB) in a purchased flash drive was given in Example 3.13 as Compute the following: a.? ?E(X) b.? ?V(X) directly from the definition c.? he standard deviation of X d.?? (X) using the shortcut formula

Answer: Step1: The pmf of the amount of memory X (GB) in a purchased flash drive was given in Example 3.13 as x 1 2 4 8 16 p(x) 0.05 0.10 0.35 0.4 0.1 a). We have to find E(x). E(x) = x p(x) = 1×0.05+ 2 ×0.1+4 ×0.35+ 8 ×0.4+ 16 ×0.1 E(x)= 6.45 b). To find V(x). Therefore, V(x) = = E[x E(x) ]2 = (x E(x) ) p(x) 2 2 2 2 = (1-(6.45) )*0.05 + (2 (6.45) ) *.1 + (4 (6.45) ) *.35 + (8 (6.45) ) * 0.4 + (16 (6.45) * 0.1 V(x) = 15.6475 c). To find the standard deviation. Standard deviation = var(x) = 15.6475 = 3.9557 Therefore, Standard deviation = 3.9557. d). To find V(x) using the shortcut formula. V(x) = E(x ) E(x) 2 2 2 Here, E(x ) = x p (x) = 1×0.05 + 4×0.1+ 16×0.35 + 64×0.4+256×0.1 = 57.25 Therefore, V(x) = E(x ) E(x) 2 2 = 57.25 - (6.45) = 15.6475 V(x) = 15.6475.