Exercise

# Updating by Bayes' rule

Suppose Madison constructs a prior for proportion of female college students who believe they are overweight, where the possible values are contained in `P`

and the respective probabilities in `Prior`

:

```
P <- c(0.5, 0.6, 0.7, 0.8, 0.9)
Prior <- c(0.3, 0.3, 0.2, 0.1, 0.1)
```

Imagine that a sample of `n = 20`

female students is selected and `y = 16`

of these students consider themselves to be overweight. The likelihood of 16 so-called "successes" in a sample of size 20 is given by the binomial density function:

```
dbinom(16, size = 20, prob = P)
```

where `P`

is the binomial probability of success.

Now you can compute Madison's posterior probabilities for the unknown proportion `P`

!

The vector of proportions `P`

and the vector of probabilities `Prior`

are both available in your workspace.

**Remember: you can use the bayesian_crank() function to implement Bayes' rule!**

Instructions

**100 XP**

- Use the
`dbinom()`

function to compute the vector of likelihoods. Store the result in`Likelihood`

. - Create a Bayesian data frame called
`bayes_df`

with variables`P`

,`Prior`

, and`Likelihood`

. - Use the
`bayesian_crank()`

function to compute the posterior probabilities. Save the result in`bayes_df`

and print it to the console. - Pass
`bayes_df`

to the`prior_post_plot()`

function to graph the prior and posterior probabilities contained in`bayes_df`

.