Homework 2

Directions

For this assignment you should record your answers in an R Markdown file and submit the compiled output as a pdf. At the start of each problem, set the seed to 8.

Homework #2 is due Friday 9/19 by 10:00pm \(~\)

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Question #1

Using a for loop and 1000 iterations, what is the probability of getting at least 10 1s on 20 rolls of a fair 4 sided-die?

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Question #2

Using the replicate function and 1000 iterations, what is the probability of getting at least 10 1s on 20 rolls of a fair 4 sided-die?

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Question #3

Write a function that does the following:

Given:

• seed (integer)
• number of replications (integer)
• probability of success (decimal between 0 and 1)
• number of iterations (integer)
• number of successes (integer)

Returns:

• probability of getting that at least that number of successes within that number of iterations.

Make sure to name it in a reasonable fashion so you could reuse it later (i.e. do not name it q3_func like I do below)

For example, if we had this function running, we could have run the Lab 2 simulation example (die is 5 or 6, coin is heads) as:

q3_func(0, 10000,.65,1000,700)

## [1] 6e-04

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Question #4

Demonstrate that your function works by

Part a Running it on the Lab 2 simulation example mentioned previously (expected value 6e-04)

Part b Running it on the example from Question 2 of this HW (hint: what is the probability of rolling a 1 on a fair 4 sided die?)

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Question #5

Turn the Question 4 from Homework 1 into a function. Then verify it works on the following test cases. Before running the test cases, how long should each of the vectors be?

x1 <- c(1,2,3, "four", 5, "six", 7, 6, 2)
x2 <- c(3, 7, "four", 2)
x3 <- c("a","b","c")
x4 <- c(1,2,3,8,9,10)
x5 <- c(4,5,6,7)
x6 <- c(1,2,3,4,5,6,7,8,9,10)
x7 <- c(5.1,4.1,3.9,7.1,6.8,55/10,75/10)