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Homework 2 solutions

# Homework 2 solutions - Statistics 5021 Homework 2(solutions...

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There are 20 total points (1 point for each part of each question). One question will be graded for correctness. This homework is due Thursday, February 10 in your lab section. 1. Deﬁne the following terms and create your own example for each: (a) Random variable Solution: A random variable is a numerical measurement of the outcome of an experiment that has yet to be performed. Example: the experiment is to measure the temperature at MSP airport this August 25th at 2:00am, let the random variable X be the temperature we will measure in degrees F. (b) Realization of a random variable Solution: The realization of a random variable is the value the random variable takes on after the experiment is performed. Example: the experiment is to ﬂip a coin 10 times independently. Let X count the number of heads we will see. I just carried out this experiment and saw 6 heads, hence x = 6 is a realization of X . 2. Let X be the number of bedrooms for an apartment we plan to randomly selected in Minneapolis. (Note that a studio apartment has 0 bedrooms). Suppose that X has the following probability mass function. x 0 1 2 3 p ( x ) 0.20 0.40 0.30 0.10 (a) Compute the mean/expected value of X Solution: Using the formula for expected value for a discrete random variable: μ X = X x xp ( x ) = 0 * 0 . 2 + 1 * 0 . 4 + 2 * 0 . 3 + 3 * 0 . 1 = 1 . 3 (b) What is the probability that this randomly selected apartment has at least one bedroom? Solution: Using the fact that x p ( x ) = 1, P ( X 1) = 1 - P ( X = 0) = 1 - 0 . 2 = 0 . 8 3. A fair coin is to be ﬂipped independently 10 times (the probability of heads on any ﬂip is 0.5). Let X count the number of “heads” we see in these 10 ﬂips. 1

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Homework 2 solutions - Statistics 5021 Homework 2(solutions...

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