You are planning a pilot study exploring student attitudes about growing income

Question

You are planning a pilot study exploring student attitudes about growing income inequality in the U.S. To begin your exploratory study, you decide to test your interview questions using a small sample of 5 students drawn randomly from a classroom of 100 students, 60 of whom are female and 40 of whom are male. Let’s define Y to be the number of females that appear in your sample. a) The random variable Y is a particular kind of discrete random variable. What kind of variable is it? b) Construct the probability distribution of Y. c) Find the mean and variance of Y using the general formulas for E(Y) and var(Y). d) Find the mean and variance of Y using the shortcut formulas for E(Y) and var(Y).

Explanation / Answer

You are planning a pilot study exploring student attitudes about growing income inequality in the U.S. To begin your exploratory study, you decide to test your interview questions using a small sample of 5 students drawn randomly from a classroom of 100 students, 60 of whom are female and 40 of whom are male. Let’s define Y to be the number of females that appear in your sample. a) The random variable Y is a particular kind of discrete random variable. What kind of variable is it? b) Construct the probability distribution of Y. c) Find the mean and variance of Y using the general formulas for E(Y) and var(Y). d) Find the mean and variance of Y using the shortcut formulas for E(Y) and var(Y).

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