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 0.15 0.25 0.30 0.25 (a) Compute E(X) (in GB). (Enter your answer to two decimal places.) GB (b) Compute V(X) (in GB2) directly from the definition. (Enter your answer to four decimal places.) GB2 (c) Compute the standard deviation of X (in GB). (Round your answer to three decimal places.) GB (d) Compute V(X) (in GB2) using the shortcut formula. (Enter your answer to four decimal places.) GB2

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fichoh fichoh · Answer 1 · 2020-10-06T07:46:49+02:00

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data :

x: ____ 1____ 2____ 4____ 8____ 16

p(x): _0.05_ 0.15__ 0.25__0.30__ 0.25

E(X) : Σ[(X). P(X)]

Σ(1*0.05) + (2*0.15) + (4*0.25) + (8*0.30) + (16 * 0.25)

= 7.75

B)

E(x) = u = 7.75

Var(X) = E[(x - u)²*p(x)] = (1 - 7.75)^2 * 0.05 + (2 - 7.75)^2 * 0.15 + (4 - 7.75)^2 * 0.25 + (8 - 7.75)^2 * 0.30 + (16 - 7.75)^2 * 0.25 = 27.7875

C)

Standard deviation (s)

s = √Var(x)

s= √27.7875

s = 5.271

D)

VAR(X) = E(X²) - (E(X))²

E(X²) = Σx²*p(x)

E(X²) = Σ(1^2 * 0.05 + 2^2 * 0.15 + 4^2 * 0.25 + 8^2 * 0.30 + 16^2 * 0.25) = 87.85

V(X) = E(X^2) - (E(X))^2 = 87.85 - 7.75^2 = 27.7875