Problem set 1

Consider the above random variable, $X$, with its associated probability distribution:

1. Draw the probability distribution function and the cumulative distribution function.

2. What is the expected value of X? That is, what is $E[X]$?

3. What is the variance of X?

Stock and Watson 2.6, 2.10, (note that I originally assigned 2.18, 3.16, but the content is covered in Week 3 - you can submit these now or with PS2)

For a randomly selected county in the United States, let $X$ represent the proportion of adults over age 65 who are employed (the elderly employment rate). Then, $X$ is restricted to a value between zero and one. Suppose that the cumulative distribution function for $X$ is given by $F(x)=3x^2-2x^3$ for $0\le x\le 1$.

1. What is the probability that the elderly employment rate is at least 0.5 (50%)?

2. What is the probability that the elderly employment rate is between 0.4 (40%) and 0.6 (60%)?