# Homework_4 - STAT 401 Spring 2016 Homework#4 To get full...

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STAT 401 Spring 2016 1 Homework #4 To get full credit show all work! Section 3.2 # 1, 2, 4 Note: In #1 from Section 3.2 show details. Section 3.3 # 1, 3 Problem A: Find the mean, variance, and standard deviation for the random variable specified in a) #2 from Section 3.2, b) #4 from Section 3.2. Problem B: In a win-win game, the player will win a monetary prize, but has to decide between the fixed price of \$1000/(E(X)+1) and the random price of \$1000/(X+1), where the random variable X is specified in # 1 from Section 3.3. Which choice would you recommend the player make and why? Problem C: A fair die is rolled twice. Let X be the maximum value to appear in the two rolls. a) What are the possible values for X? b) Find and plot the pmf of X. c) Find and plot the cdf of X. Problem D: Refer to the random variable X from Problem C: a) Find the probability that the maximum value in the two rolls is at least 3, but no more than 5. b) If the maximum is at least 3, what is the probability it’s at most 5?

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Unformatted text preview: c) Find the mean, variance, and standard deviation of X. Problem E: The thickness of wood paneling (in inches) that a customer orders is a random variable with the following cumulative distribution function (cdf): ? ° (±) = { ± < 1/8 0.2 1/8 ≤ ± < 1/4 0.9 1/4 ≤ ± < 3/8 1 ± ≥ 3/8 a) Arrange the cdf ? ° (±) in a table and plot it. STAT 401 Spring 2016 2 b) Determine the pmf of X. Arrange it in a table. c) Find °(−1.7 < log(±) < −0.7) . (Note: log(∙) is the natural log, or ln(∙) ). d) Find ?(log(±) ) and comment whether this value is equal to or less than or greater than log(?(±)) . Problem E: [BONUS] Let X be the number of jobs held during past year for students at a school. The incomplete pmf and cdf of X are given in the tables below: x 0 1 2 3 4 p(x) 0.37 0.15 x 0 1 2 3 4 F(x) 0.14 0.80 0.95 Complete the tables by finding the five missing entries. Provide details about how you determine each of them....
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