hw05_Distributions.Rmd

---

title: HW05--Other Distributions
subtitle: Binomial and Geometric
author: NAME HERE
date: Fall 2020
output:
  html_document:
    highlight: tango
    theme: spacelab
    toc: yes

---

Turn in the html file to Canvas on Friday before might night. Some of the questions will require you to make code blocks but some won't. Read the questions carefully.

Questions

Summary

1. What is a trial? (1 point)

A trial is an essentially and experiment

2. Describe when a binomial distribution is applicable. Make sure you describe in terms of the proper variables i.e. x, n, etc. (3 points)

A binomial distribution is applicable when he number of trials and the probability are already set. The purpose o a binomial distribution is to find the number of sucseses(x) out of the number of trials(n)

3. Describe when a geometric distribution is applicable. Make sure you describe in terms of the proper variables i.e. q, p, etc. (3 points)

Geometric distributions are applicable when you only have one success for any number of failures. The number of failures is represented by the variable (x). dgeom(x,p) finds the probability after x failures. pgeom(q,p) finds the probability of success before or up to Q failures.

4. How are the binomial and geometric distributions different? (2 points)

Binomial is when we want to count the number of successes out of a number of trials. Geometric happens when 1 success comes before a number of failures and we don't know the number of trials

Examples

1. In the game of craps, two dice are rolled for the sum of the two numbers. Rolling a "2, 3, 12" is a failure which is called "craps". Rolling a "7 or 11" is a success which is called a "natural". Anything else i.e. "4, 5, 6, 8, 9, and 10" is neither and the player rolls again. Can the number of "successes" while playing 10 rounds of craps be modelled by the binomial distribution? Why or why not. (3 points)

It would be a binomial distribution because they count the number of successes in a number of trials. Here, we are given situations where it is neither success or failure, there is no variable for rerolls though since it is a binomial distribution.

2. Give an example of a problem that looks like one should use a geometric distribution but for which you actually can't. (2 points)

if the probability to bowl a strike is 1/3, what is the probability that I bowl a strike on my 5th attempts after not bowling a strike on my first 4

Calculations

1. The Soyuz rocket has had about 1,700 launches with 60 launch failures since 1966 which is one of the best reliability rates in the Space Industry. Your company needs to launch five satellites into orbit. What is the probability that at least three of the five are successful? Explain how you reached your conclusion. (5 points)

100 - (60/1700*100)
pbinom(2,5,0.96)
100 - .06

2. Consider the game of craps. Suppose that rolling a "7 or 11" is a success but everything else is a failure. What is the probability that your first failure is after 10 rolls? (5 points)

ANSWER HERE