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A random variable Y has the following distribution
Chapter 4, Problem 9E(choose chapter or problem)
A random variable Y has the following distribution function:
\(F(y)=P(Y \leq y)=\left\{\begin{array}{ll} 0, & \text { for } y<2 \\ 1 / 8, & \text { for } 2 \leq y<2.5, \\ 3 / 16, & \text { for } 2.5 \leq y<4, \\ 1 / 2 & \text { for } 4 \leq y<5.5, \\ 5 / 8, & \text { for } 5.5<y<6, \\ 11 / 16, & \text { for } 6 \leq y<7, \\ 1, & \text { for } y \geq 7 \end{array}\right.\)
a. Is Y a continuous or discrete random variable? Why?
b. What values of Y are assigned positive probabilities?
c. Find the probability function for Y.
d. What is the median, \(\phi_{.5}\), of Y?
Questions & Answers
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QUESTION:
A random variable Y has the following distribution function:
\(F(y)=P(Y \leq y)=\left\{\begin{array}{ll} 0, & \text { for } y<2 \\ 1 / 8, & \text { for } 2 \leq y<2.5, \\ 3 / 16, & \text { for } 2.5 \leq y<4, \\ 1 / 2 & \text { for } 4 \leq y<5.5, \\ 5 / 8, & \text { for } 5.5<y<6, \\ 11 / 16, & \text { for } 6 \leq y<7, \\ 1, & \text { for } y \geq 7 \end{array}\right.\)
a. Is Y a continuous or discrete random variable? Why?
b. What values of Y are assigned positive probabilities?
c. Find the probability function for Y.
d. What is the median, \(\phi_{.5}\), of Y?
ANSWER:Step 1 of 5
A random variable Y has the given distribution function.
\(F(y)=P(Y \leq y)=\left\{\begin{array}{ll} 0, & \text { for } y<2 \\ 1 / 8, & \text { for } 2 \leq y<2.5, \\ 3 / 16, & \text { for } 2.5 \leq y<4, \\ 1 / 2 & \text { for } 4 \leq y<5.5, \\ 5 / 8, & \text { for } 5.5<y<6, \\ 11 / 16, & \text { for } 6 \leq y<7, \\ 1, & \text { for } y \geq 7 \end{array}\right.\)
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