In: Statistics and Probability
(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).