STAT 20: Introduction to Probability and Statistics

Agenda

Brief lecture on probability distributions and random variables

Review quiz 3

Concept questions

Break

Handout: PS 4.1 (random variables)

Probability and quiz review

Concept Questions

01:00

Is the following random variable binomial (if so, what are \(n\) and \(p\)?), hypergeometric (if so , what are \(N\), \(G\), and \(n\)?), or neither?

Roll a fair ten-sided die 20 times. Let \(X\) be the number of times we roll a multiple of 3.

Binomial, hypergeometric, or neither?

01:00

Is the following random variable binomial (if so, what are \(n\) and \(p\)?), hypergeometric (if so , what are \(N\), \(G\), and \(n\)?), or neither?

Poll 1,000 Chicago residents and ask them if they voted for Lori Lightfoot in the mayoral election. Let \(X\) be the number of people who respond “Yes”. The population of Chicago is about 2.7 million.

Binomial, hypergeometric, or neither?

01:00

Is the following random variable binomial (if so, what are \(n\) and \(p\)?), hypergeometric (if so , what are \(N\), \(G\), and \(n\)?), or neither?

A six-sided die is tossed two times and the sum of the faces showing is \(8\). Let \(X\) be 1 if the sum is \(8\) and \(0\) otherwise.

Binomial, hypergeometric, or neither?

01:00

Is the following random variable binomial (if so, what are \(n\) and \(p\)?), hypergeometric (if so , what are \(N\), \(G\), and \(n\)?), or neither?

A bag that has 6 pieces of fruit: 2 mangoes, 3 apples, and 1 orange. I reach into the bag and draw out one fruit at a time, selecting each fruit at random (so they are equally likely). Let \(X\) be the number of draws until and including the first time I draw a apple.

Binomial, hypergeometric, or neither?

01:00

You have \(10\) people with a cold and you have a remedy with a \(20\%\) chance of success. What is the chance that your remedy will cure at least one sufferer? (Let \(X\) be the number of people cured among the 10. We are looking for the probability that \(X \ge 1\))

What is the chance that at least one person is cured?

03:00

Roll a pair of fair six-sided dice and let \(X = 1\) if the dice land showing the same number of spots, and \(0\) otherwise. For example, if both dice land \(2\), then \(X = 1\), but if one lands \(2\) and the other lands \(3\), then \(X = 0\).