CS1951A | Statistics Pre-Quiz

statistics pre-quiz

This quiz is designed to assess your knowledge of probability and statistics. We recommend that you work out these problems using pen and paper. Feel free to use any resources you like, although using something like WolframAlpha will not be a good judge of your skills.

probability

Imagine that you have a box with 2 blue marbles and 5 red marbles in it.

  1. What is the chance of drawing a blue marble?
  2. What is the chance of drawing a red and a blue marble if you sample if you sample with replacement? (Order doesn't matter.)
  3. Imagine drawing all the marbles from the box. How many different orderings of drawn marbles are possible?
  4. Imagine you now have two boxes; the first is the same as above, but the second has 4 blue marbles and 3 red marbles. You draw from one of the boxes at random, and see that you have picked a blue marble. What is the chance that you drew the marble from the first box?

Now imagine that you have a six-sided die and a ten-sided die.

  1. What is the expected value of rolling the six-sided die?
  2. What is the expected value of rolling both dice?
  3. What is the variance of the sum of both die?
  4. What is the chance of the sum of the two dice being 4?
  5. Imagine that I tell you that I have rolled a 4 with one of the dice. It is twice as likely that for any roll I will use the ten-sided die. What is the chance that I used the ten-sided die for this roll?

statistics

Here is a sample from a distribution: \(\{-2, -1, 3, 3, 5, 6, 8, 10, 11\}\).

  1. What is the mean of the sample?
  2. What is the median?
  3. What is the mode?
  4. What is the standard deviation?

Consider a continuous normal distribution with \(\mu = 3\) and \(\sigma = 3\).

  1. What is the variance?
  2. What is the median?
  3. What is the probability of sampling from the distribution and getting \(0\)?
  4. What is the probability of getting less than \(-1\)?

solutions

Solutions available in this PDF. If you would like an explanation to these solutions, please visit TA hours.