Problem 8: The Rayleigh density of random variable X is fx(x) = (x - a)e 0 b if x ≥ a if x

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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(x-a)²
bif x ≥ a
Problem 8: The Rayleigh density of random variable X is fx(x) =
-(x − a)e
0
if x <a
a. Find the distribution function F(x).
b. The lifetime of a system expressed in weeks is a Rayleigh random variable X for whicl
a = 0,b= 400. What is the probability that the system will not last a full week? What is the probability
that the system will exceed one year?
2-6
b
Transcribed Image Text:(x-a)² bif x ≥ a Problem 8: The Rayleigh density of random variable X is fx(x) = -(x − a)e 0 if x <a a. Find the distribution function F(x). b. The lifetime of a system expressed in weeks is a Rayleigh random variable X for whicl a = 0,b= 400. What is the probability that the system will not last a full week? What is the probability that the system will exceed one year? 2-6 b
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