The pmf of the amount of memory x (gb) in a purchased flash drive is given as the following. x 1 2 4 8 16 p(x) 0.05 0.10 0.30 0.45 0.10 (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

a. Expected value is defined by

so we get

b. Variance is defined by

so with the expectation found above, we have

(by definition of expectation)

c. Standard deviation is the square root of variance:

d. I assume "shortcut formula" refers to

which is easily derived from the definition of variance. We have (by def. of expectation)

and so the variance is again

as expected.

answer: the answer is 30 miles per hour.

ft/s -> mphmph = ft/s 1.466667mph = 44 divided by 1.466667mph = 30.00000

- r3ktforgood ☕