Stat problems for Wed, Feb 9

  1. Consider the table shown below.
    1. What number should the ? if we'd like the table to represent a discrete random variable?
    2. Compute the mean of the resulting random variable.
    3. Compute the standard deviation of the resulting random variable.
  2. Let's suppose that 3% of the population has green eyes. We draw a sample of 66 people and count the number of them with green eyes to produce a random variable $X$.
    1. What's the expectation of $X$?
    2. What's the standard deviation of $X$?
    3. $x_i$ 1 3 5 6
    $p_i$ 0.1 0.3 ? 0.1
  3. You can play the following game for \$1: I'll deal you 4 cards from a well-shuffled deck. If your hand is exactly the Jack, Queen, King, Ace of Hearts, you win \$10000. Let's call your earnings $X$. What is the expected value of $X$?