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.

72 is the answer to this problem

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq