question d and e 1) Probability density function of Rayleigh distributed x random variable given asfollowsfx(x) = kxex20.a) Find k.b) Find the mean (E[X]), the second moment (E[X²]) and the variance (o ) ofc) 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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Description: question d and e 1) Probability density function of Rayleigh distributed x random variable given asfollowsfx(x) = kxex20.a) Find k.b) Find the mean (E[X]), the second moment (E[X²]) and the variance (o ) ofc) Find the cumulative distribution function

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question d and e

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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