Homework 2 solutions

Homework 2 solutions - Statistics 5021 Homework 2...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/06/2011 for the course STAT 5021 taught by Professor Staff during the Spring '08 term at Minnesota.

Page1 / 6

Homework 2 solutions - Statistics 5021 Homework 2...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online