Question

12.-14 points DevoreStat9 3.E.029 The pmf of the amount of memory X (GB) in a purchased flash drive is given as the following. 1 2 4 83 16 p(x) 0.05 0.15 0.30 0.450.05 (a) Compute E(X). (Enter your answer to two decimal places.) GB (b) Compute V(X) directly from the definition. (Enter your answer to four decimal places.) (c) Compute the standard deviation of X. (Round your answer to three decimal places.) GB (d) Compute V(x) using the shortcut formula. (Enter your answer to four decimal places.) Need Help?Read It Talk to a Tutor

Answer 1

a)

$E(X) = \sum xP(x) = 1*0.05+2*0.15+4*0.30+8*0.45+16*0.05 = 5.95$

b)

$V(X) = \sum (X-\mu )^{2}P(x)$

$\sigma ^{2} =V(X) = 11.6475$

c) $\sigma= \sqrt{11.6475} = 3.4128$

d)

$\sigma ^{2} =E(X^{2}) -\left \{ E(X) \right \}^{2}$

$E(X^{2}) = \sum x^{2}P(x) = 1^{2}*0.05+2^{2}*0.15+4^{2}*0.30+8^{2}*0.45+16^{2}*0.05$

$\sigma ^{2} =V(X) = 47.05-5.95^2 = 11.6475$