Homework 1 solutions

Homework 1 solutions - Statistics 5021 Homework 1...

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Unformatted text preview: Statistics 5021 Homework 1 (solutions) There are 20 total points (1 point for each part of each question excluding question 1, which is worth 0 points). One question will be graded for correctness. This homework is due Thursday, February 3 in your lab section. 1. The purpose of this homework problem is for you to try (you do not need to write/hand- in anything for this problem) a few commands in R . If you wish to have R installed on your personal computer (which I recommend) you may download it from: http://streaming.stat.iastate.edu/CRAN/ If you would prefer to use R through a website, you can access it at https://rweb.stat.umn.edu/Rweb/ using your x.500 UM Internet ID. Try the following commands (note that R is case sensitive): (a) hist(rnorm(n=10000, mean=68, sd=4), freq=FALSE) (b) hist(runif(n=10000, min=60, max=75), freq=FALSE) 2. The experiment is to flip two coins. (a) Write down the sample space S , that is, list all possible outcomes of this experi- ment. Solution: S = { HH,HT,TH,TT } (b) Let A be the event that we see heads on the second flip. Write down the outcomes in A . Solution: A = { TH,HH } (c) Let B be the event that we see at least one heads in the two flips. Write down the outcomes in B Solution: B = { HH,HT,TH } 1 (d) Write down the outcome(s) in the event A B . Solution: A B = A = { TH,HH } (e) Let C be the event that we see tails on both flips. Write down the outcome(s) in C . Solution: C = { TT } (f) If all outcomes in this experiment are equally-likely, compute P ( A B ). Solution: Using the equally likely rule: P ( A B ) = num. of outcomes in A B num. of outcomes in S = 2 / 4 = 1 / 2 (g) If all outcomes in this experiment are equally-likely, compute P ( C B ) Solution:...
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Homework 1 solutions - Statistics 5021 Homework 1...

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