6. Let X be a random variable having pdf :{ (a) (b) (d) fx(x) = A exp{-X(x-μ)} 0 Show that fx(x) is a legitimate pdf. Find the cdf of X. if x > μ, otherwise. Using the definition of E[X], find the mean of X. Find the mgf Mx (t) of X, and use it to find u.

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6. Let X be a random variable having pdf
fx (x) = {
(a)
(b)
(c)
(d)
A exp{-X(x-μ)}
0
Show that fx(x) is a legitimate pdf.
Find the cdf of X.
if x > μ,
otherwise.
Using the definition of E[X], find the mean of X.
Find the mgf Mx (t) of X, and use it to find u.
Transcribed Image Text:6. Let X be a random variable having pdf fx (x) = { (a) (b) (c) (d) A exp{-X(x-μ)} 0 Show that fx(x) is a legitimate pdf. Find the cdf of X. if x > μ, otherwise. Using the definition of E[X], find the mean of X. Find the mgf Mx (t) of X, and use it to find u.
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