Ex3: The diameter of a particle of contamination (in micrometers) is modeled with the probability density function f(x) = - for x>1. с 3 X Determine the following: a/ c and P(X<2) b/ P(X>4) and P(2< X <8 c/ Mean and variance of X

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Ex3: The diameter of a particle of contamination (in
micrometers) is modeled with the probability
density function f(x) = for x>1.
C
3
x²
Determine the following:
a/ c and P(X<2) b/ P(X > 4) and P(2< X <8)
c/ Mean and variance of X
d/x such that P(X<x)=0.95
e/ The cumulative distribution function F(x)
t
Transcribed Image Text:Ex3: The diameter of a particle of contamination (in micrometers) is modeled with the probability density function f(x) = for x>1. C 3 x² Determine the following: a/ c and P(X<2) b/ P(X > 4) and P(2< X <8) c/ Mean and variance of X d/x such that P(X<x)=0.95 e/ The cumulative distribution function F(x) t
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