Let X be a random variable of the mixed type having the cdf F(x) = 0, x < 0, x2 4 , 0 x
Chapter 3, Problem 3.4-7(choose chapter or problem)
Let X be a random variable of the mixed type having the cdf
\(F(x)=\left\{\begin{array}{ll}0, & x<0 \\\frac{x^{2}}{4}, & 0 \leq x<1 \\\frac{x+1}{4}, & 1 \leq x<2 \\1, & 2 \leq x\end{array}\right.\)
(a) Carefully sketch the graph of F(x).
(b) Find the mean and the variance of X.
(c) Find P(1/4 < X < 1), P(X = 1), P(X = 1/2), and \(P(1/2 \le X < 2)\).
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