---
title: "Application Exercise: Practice with Binomial and Poisson"
author: "Your Name Here"
date: "Today's Date Here"
format: html
---

## Setup

Update your name and today's date in the YAML above.

## A Clinical Trial: Binomial Example

Suppose 5 people receive a new vaccine. From clinical trial data, the probability that any individual experiences a mild side effect (e.g., sore arm, mild fever) is 0.2.  
Let $X$ be the number of people (out of 5) who experience a mild side effect.  
Then $X \sim \text{Binomial}(n=5, p=0.2)$.

### Exercise 1

What is the probability that exactly 2 out of 5 people experience a mild side effect? Use the `dbinom` function to compute your answer and provide a 1-sentence conclusion.

```{r}
# type code here
```

[type response here]

## Exercise 2

What is the probability that at least 1 out of 5 people experiences a mild side effect?
(Hint: Use the complement rule: $P(X \geq 1)=1−P(X=0)$). Use the `dbinom` function to compute your answer and provide a 1-sentence conclusion.

```{r}
# type code here
```
[type response here]

## Hospital Visits: Poisson Example

Suppose that in a hospital emergency department, the average number of asthma-related visits per hour is 3. Let $Y$ be the number of asthma visits in one hour. Then $Y \sim Poisson(\lambda=3)$

### Exercise 3

What is the probability that in a given hour, exactly 5 asthma patients arrive? Use the `dpois` function to compute your answer and provide a 1-sentence conclusion.

```{r}
# type code here
```

[type response here]

## Submission

Render to PDF and submit on Canvas > Assignments.