---
title: "Lab 2"
author: "Name here"
output: html_document
---

Please use D2L to turn in both the HTML output and your R Markdown file in.

## Q1. (10 pts) 
Simulate the Mean and Variance of samples from a uniform(0,1) distribution.

## Q2 (15 pts)
Recall the mixture distribution from HW1
```{r, echo=F}
inches <- seq(0,10, by= .01)
density <- dgamma(seq(0, 10, by=.01), 5, 1.5) * .5
density[1] <- density[1] + .5
plot(inches, density, type='l', lwd=2, main='Probability of Snow Tomorrow ', xlab = 'Inches', ylab = '')
```

### a (5 pts)
Estimate the 95% HDI for this distribution.

### b (10 pts)
Use the code below to take samples and estimate the mean and variance of this distribution.

```{r}
num.samples <- 1000
samples <- ifelse(runif(1000) < .5, 0, 1)
samples[samples == 1] <- rgamma(sum(samples),5,1.5)
```