Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

A statistics students suggests using a binomial model for the number of games out of these ten that the Packers will win. Provide one

image text in transcribed

A statistics students suggests using a binomial model for the number of games out of these ten that the Packers will win. Provide one or more reasons for why this model may not meet all of the assumptions for a binomial model. > [Write your answer here] ###7 Imagine this two-stage process to create a random variable $X$. In the first step, select a coin at random from a large bag of coins where each coin as a different head probability, $P$. The distribution of $P$ is uniform between 0 and 1, meaning that the density has the function $f(p) = 1$. Then, after selecting a specific coin where the random variable $P$ has the value $p$, toss the coin 9 times and count the number of heads. Let $X$ be the number of heads. The *conditional* distribution of $X$ given a specific value of $P=p$, is binomial, $X\,\mid\, P=p \sim \text{Binomial}(9,p)$. But the *unconditional* distribution of $X$ is not binomial: it is instead has a distribution formed by averaging together many different binomial distributions, each with $n=9$, but with different values of $p$. We will use simulation to try to guess the distribution of $X$. This block of code generates $B = 1,000,000$ random realizations of $P$ and $X$. We can then calculate sample statistics of these simulated values as estimates of the values that could be found using analytical methods. The columns are `n`, 9 for each row, `p`, a head probability selected uniformly between 0 and 1, and `x`, a single generated value of $X$ selected at random from a binomial distribution with `n` and `p` for each given row. ***`{r} set.seed(2022) B = 1000000 prob7 = tibble( n = rep(9, B), p = runif(B), x=rbinom(B, n, p) ### 7A Use geom_density() to display an estimated graph of the density of $P$. We know that the exact density is uniform between 0 and 1. Does the estimated density approximate the exact density well? ***{r} ### 7B Calculate the mean and standard deviation of the values in the column `p`.

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Probability and Random Processes With Applications to Signal Processing and Communications

Authors: Scott Miller, Donald Childers

2nd edition

123869811, 978-0121726515, 121726517, 978-0130200716, 978-0123869814

More Books

Students also viewed these Mathematics questions

Question

Find the derivative f(x) = 2x3 2x2 +9

Answered: 1 week ago

Question

Describe why it is important to validate a data model. AppendixLO1

Answered: 1 week ago