STAT537/hw2.Rmd at master · runawayhorse001/STAT537 · GitHub

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---
title: "Homework #2"
author: "Ming Chen & Wenqiang Feng"
date: "2/2/2017"
output: html_document
---
## You can also get the [PDF format](./pdf/HW2.pdf) of Wenqiang's Homework.

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

## Q1

* a. $n=10, \pi=0.2, y=3$

```{R}
P = dbinom(3, 10, 0.2)
P
```

* b. $n=4, \pi=0.4, y=2$

```{R}
P = dbinom(2, 4, 0.4)
P
```

* c. $n=16, \pi=0.7, y=12$

```{R}
P = dbinom(12, 16, 0.7)
P
```


## Q2

* a.   $P(y\leq4)$

```{R}
P = pbinom(4, 8, 0.4)
P
```

* b.   $P(y>4) = 1 - P(y\leq4)$

```{R}
P = 1 - pbinom(4, 8, 0.4)
P
```

* c.   $P(y\leq7) = P(y\leq7) - P(y=7)$

```{R}
P = pbinom(7, 8, 0.4) - dbinom(7, 8, 0.4)
P
```

* d.   $P(y\geq6) = 1 - P(y\leq6) + P(y=6)$

```{R}
P = 1 - pbinom(6, 8, 0.4) + dbinom(6, 8, 0.4)
P
```


## Q3 Exercise 4.46

* a. two are rated as outstanding
    + P(outstanding) = 0.1
    + P(X=2) = `dbinom(2, 10, 0.1)` = `r dbinom(2, 10, 0.1)`

```{R}
dbinom(2, 10, 0.1)
```

* b. two or more are rated as outstanding
    + P(outstanding) = 0.1
    + $P(X\geq2) = 1 - P(X\leq1)$ = `1 - pbinom(1, 10, 0.1)` = `r 1 - pbinom(1, 10, 0.1)`

```{R}
1 - pbinom(1, 10, 0.1)
```


* c. eight of the ten are rated either outstanding or excellent
    + P(outstanding or excellent) = 0.1 + 0.75 = 0.85
    + P(X=8) = `dbinom(8, 10, 0.85)` = `r dbinom(8, 10, 0.85)`

```{R}
dbinom(8, 10, 0.85)
```

* d. none of the trainees is rated as unsatisfactory
    + P(unsatisfactory) = 0.05
    + P(X=0) = `dbinom(0, 10, 0.05)` = `r dbinom(0, 10, 0.05)`

```{R}
dbinom(0, 10, 0.05)
```