If, as in Exercise 4.19, Y has distribution function find

Chapter 4, Problem 25E

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QUESTION:

If, as in Exercise 4.19, Y has distribution function

\(F(y)=\left\{\begin{array}{ll}
0, & y \leq 0, \\
\frac{y}{8}, & 0<y<2, \\
\frac{y^{2}}{16}, & 2 \leq y<4, \\
1, & y \geq 4,
\end{array}\right.\)

find the mean and variance of Y.

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QUESTION:

If, as in Exercise 4.19, Y has distribution function

\(F(y)=\left\{\begin{array}{ll}
0, & y \leq 0, \\
\frac{y}{8}, & 0<y<2, \\
\frac{y^{2}}{16}, & 2 \leq y<4, \\
1, & y \geq 4,
\end{array}\right.\)

find the mean and variance of Y.

ANSWER:

Step 1 of 3

We have random variable Y with the distribution function:

\(F(y)=\left\{\begin{array}{ll}
0, & y \leq 0, \\
\frac{y}{8}, & 0<y<2, \\
\frac{y^{2}}{16}, & 2 \leq y<4, \\
1, & y \geq 4,
\end{array}\right.\)

We need to find mean and variance of of Y.

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