e. A continuous random variable X has cdf
e. A continuous random variable X has cdf
$$ F(x)=\left\{\begin{array}{cc} a & x \leq 0 \\ x^{2} & 0< x \leq 1 \\ b & x>1 \end{array}\right. $$
a. Determine the constants a and b.
b. Find the pdf of X. Be sure to give a formula for fx(X) that is valid for all x.
c. Calculate the expected value of X.
Homework Answers
a)
F(-infinity) = 0
hence a = 0 ,
F(infinity) = 1
hence
b = 1
b)
f(x) = d/dx F(x) = 2x
hence
f(x) = 0 x < 0
= 2x 0< x< 1
= 0 x> 1
c)
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