2. Let X denote the amount of space occupied by an article placed in a 1 - fr' packing container. The pdf of X is [90x*(1 – x) 0

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Solve d, e and f
2. Let X denote the amount of space occupied by an article placed in a 1 - fr packing container.
The pdf of X is
f(x) = { 90x*(1 – x) 0<x<1
otherwise
(a) Obtain the cdf of X
(b) What is P(X < 0.5)?
(c) What is P(0.25 < X < 0.5)?
(d) What is the median of the distribution?
(e) Compute E(X)
(f) Compute V(X)
Transcribed Image Text:2. Let X denote the amount of space occupied by an article placed in a 1 - fr packing container. The pdf of X is f(x) = { 90x*(1 – x) 0<x<1 otherwise (a) Obtain the cdf of X (b) What is P(X < 0.5)? (c) What is P(0.25 < X < 0.5)? (d) What is the median of the distribution? (e) Compute E(X) (f) Compute V(X)
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