+ 10 points DevoreStat93. E.029 The pmf of the amount of memory X (GB) in a purc

Question

+ 10 points DevoreStat93. E.029 The pmf of the amount of memory X (GB) in a purchased flash drive is given as the following. 2 4 8 16 p(x) 0.05 0.10 0.30 0.40 0.15 (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.) GB2 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.) GB2 Need Help? Read ItTalk to a Tutor Submit Answer Save Progress Practice Another Version

Explanation / Answer

(a) E(x) = xf(x)

= 1*0.05 + 2*0.10 + 4*0.30 + 8*0.40 + 16*0.15

= 7.05

(b) V(x) = (x - E(X))2 f(x)

= (1 - 7.05)2 * 0.05 + (2 - 7.05)2 * 0.10 + (4 - 7.05)2 * 0.30 + (8 - 7.05)2 * 0.40 + (16 - 7.05)2 * 0.15

= (-6.05)2 * 0.05 + (-5.05)2 * 0.10 + (-3.05)2 * 0.30 + (0.95)2 * 0.40 + (8.95)2 * 0.15

= 19.5475

(c) Standard deviation = 19.5475 = 4.421

(d) V(x) = x2f(x) - (E(X))2

= 1*0.05 + 4*0.10 + 16*0.30 + 64*0.40 + 256*0.15 - 7.052

= 19.5475

x 1 2 4 8 16 f(x) 0.05 0.10 0.30 0.40 0.15

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