(15 pts) Suppose that the continuous random variable X has pdf ?(?) = { ?; 0...

(15 pts) Suppose that the continuous random variable X has pdf
?(?) = {
?; 0 < ? < 2 2?; 5 < ? < 10 0; otherwise
a) Determine the value of c that makes this a legitimate pdf.

b) Sketch a graph of this pdf.

c) Determine the cumulative distribution function (cdf) of X.

d) Sketch a graph of this cdf.

e) Calculate ? = ?(?) and ? = ??(?).

f) What is ?(? = ?)?

g) Compute ?(? − ? < ? < ? + ?).

h) Find the median of X

i) Let ? = √?. Calculate E(Y).

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Expert Solution

orchestra answered 1 year ago

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