6) Let X have the pdf given by: f(x) = { c(1-x)x² 0

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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6) Let X have the pdf given by:
f(x)=
c(1-x)x²
0
a) Find the value of c.
b) Find the CDF of X, Fx(x).
c) Find the values of Fx(-1), Fx(0.5), and Fx(1).
d) Find E(X).
e) Find P(0≤x≤ 0.5).
f) Find P(X>0.5 | X > 0.1).
0<x< 1
otherwise
Transcribed Image Text:6) Let X have the pdf given by: f(x)= c(1-x)x² 0 a) Find the value of c. b) Find the CDF of X, Fx(x). c) Find the values of Fx(-1), Fx(0.5), and Fx(1). d) Find E(X). e) Find P(0≤x≤ 0.5). f) Find P(X>0.5 | X > 0.1). 0<x< 1 otherwise
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