1. Imagine a person who wants to find a job within two months.

a. Explain why the eventual outcome (finding a job or not finding a job) can be viewed as a random variable.

b. What distribution can be used to characterized this variable? Be as specific as possible.

2. Suppose that the population of employed people in a small town is 2,000. Among the employed, 500 employees receive the hourly wage of $8 per hour, 1100 employees receive $10 per hour, and 400 employees receive $12 per hour. Let W denote the hourly wage rate of a randomly drawn person from the employed population.

a. Find the probability that W is equal to $8. Find Pr(W = 10), Pr(W = 12).

b. Find the expected wage, E(W).

c. Find Var(W).

3. Let X1 and X2 be independent random variables with E(X1) = 3, E(X2) = 4, Var(X1) = 9 and Var(X2) = 4. Let Z = 2.5X1 − 0.5X2 denote a new random variable.

a. Find E(Z) and Var(Z).

b. Suppose now that X1 and X2 are not independent, and Cov(X1, X2) = 3. Find Var(0.5X1 − X2).

4. In a sample of 200 houses, the sample average price was found to be $196,340. Assume the variance of house prices is 830,000,000. Let random variable X denote house price, and µ denote its unknown population mean, E(X) = µ. For each of the following questions, formulate the appropriate null and alternative hypotheses, perform the test, and interpret test results:

a. Is the average house price below $200,000?

b. Is the average house price above $200,000?

c. Is the average house price different from $200,000?

5. A random sample of 100 FSU students included 58 females and 42 males. Let G denote a random variable equal 1 if the person is a female and 0 if the person is a male.

a. Find the sample average, G¯, and sample variance, S 2 G, of variable G.

b. Are FSU students predominantly female? Formulate and test the corresponding null and alternative hypotheses to answer this question, interpret results.

c. Is gender composition of FSU students perfectly balanced? Formulate and test the corresponding null and alternative hypotheses to answer this questions, interpret results.