1) Probability density function of Rayleigh distributed X random variable given as follows fx(x) = kxe x20. a) Find k. b) Find the mean (E[X]), the second moment (E[X²)) and the variance (ơ; ) of c) Find the cumulative distribution function of X. d) Find Pr{1/2

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 32EQ
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1) Probability density function of Rayleigh distributed x random variable given as
follows
fx(x) = kxe
x20.
a) Find k.
b) Find the mean (E[X]), the second moment (E[X²]) and the variance (o ) of
c) Find the cumulative distribution function of X.
d) Find Pr{1/2< X <1}.
e) If Y = X² , find the PDF and CDF of Y.
Transcribed Image Text:1) Probability density function of Rayleigh distributed x random variable given as follows fx(x) = kxe x20. a) Find k. b) Find the mean (E[X]), the second moment (E[X²]) and the variance (o ) of c) Find the cumulative distribution function of X. d) Find Pr{1/2< X <1}. e) If Y = X² , find the PDF and CDF of Y.
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