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Let X has the probability density function (pdf) f(x)={C1, if 0 < x ≤ 1, C2x, if1<x≤4, 0,...

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Statistics

Let X has the probability density function (pdf)

f(x)={C1, if 0 < x ≤ 1,

C2x, if1

0, otherwise.

Assume that the mean E(X) = 2.57.

(a) Find the normalizing constants C1 and C2.

(b) Find the cdf of X, FX.

(c) Find the variance Var(X) and the 0.28 quantile q0.28 ofX.

(d)LetY =kX. Find all constants k such that Pr(1

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