```{r echo=FALSE}
opts_chunk$set(echo=TRUE, tidy=FALSE)
```

WASSUP
===========
(c) Gail Gong 2013

03a More R sharpening
===========

### 1. Review some functions that might be useful

```{r review, eval=FALSE}
setdiff(1:10, c(3, 1, 4, 100))
sort(c(3, 1, 4, 1, 5, 9))
1:3 %in% c(3, 1, 4, 1, 5, 9)
any(c(TRUE, FALSE))
any(c(FALSE, FALSE))
all(c(TRUE, FALSE))
all(c(TRUE, TRUE))
ifelse(c(TRUE, FALSE, TRUE, FALSE), c(1, 2, 3, 4), c(10, 20, 30, 40))

seats = c("", "", "o", "", "", "o", "o", "o")
success = TRUE
data.frame(t(c(s = seats, success = success)))

look = data.frame(chairs = letters[1:7], score = sort(c(3, 1, 4, 1 ,3, 4, 4)))
look
look[look$score >= 4, ]
```


# AAAA

I repeatedly roll a 6-sided die and I record the result in `roll`.  I also keep a `runningTotal`.  Write code to find the number of rolls it takes to have a `runningTotal` at least `13`. (I want the smallest `index` such that `runningTotal >= 13`.)

Your code should work if I give you a different set of rolls.


```{r look}
set.seed(1)
NRolls = 13
index = 1:NRolls
roll = sample(1:6, size = NRolls, replace = TRUE)
runningTotal = cumsum(roll)
look = data.frame(index, roll, runningTotal)
look
```


```{r aaaa}
smallest = c(look$index[look$runningTotal >=13])
smallest[1]
```

### 2. Review `while`, and my example has some useful ideas.

```{r whileExample, eval=FALSE}
rollHistory = c()
runningTotal = 0
gameOver = runningTotal >= 13
while(!gameOver){
  roll = sample(1:6, size = 1)
  rollHistory = c(rollHistory, roll)
  runningTotal = runningTotal + roll
  gameOver = (runningTotal >= 13)
  print(data.frame(runningTotal, gameOver, t(c(roll = rollHistory))))
  }
rollHistory
runningTotal
data.frame(rollHistory, look = cumsum(rollHistory))
```

# BBBB

What does this while loop (above) do?

The `while` loop checks `gameOver`; if `gameOver == FALSE`, go inside the curly braces and muck in there; if `gameOver == TRUE` exit the `while`.  Do you agree? Yes.

### 3. `sample` with the `prob` option.

```{r sample}
pRed = 0.9
oneHundredBalls = sample(c("blue", "red"),
  size = 100, replace = TRUE, prob = c(1-pRed, pRed))
table(oneHundredBalls)
```

# CCCC

I have a biased coin that has probability `0.8` of coming up Heads.  Write code that simulates tossing this coin 10 times.  Show me the tosses and show me the proportion that came up heads.

```{r cccc}
pHeads = 0.8
toss = sample(c("tails", "heads"), size =10, replace = TRUE, prob = c(1-pHeads, pHeads))
toss
table(toss)
proportion = sum(toss == "heads")/10
proportion
```


### 4. Bayes rule

At a widget factory there are two machines.  Quicky is faster than Careful so it produces 60 percent of the widgets.  The proportion of widgets made by Quicky that are defective is 10 percent, and the proportion of widgets made by Careful that are defective is 4 percent.  If a widget is found to be defective, what is the probability it was made by Quicky?

I will rewrite Bayes rule (see the lecture notes on Conditional Probabilities) substituting the notation here.

```
M1 = Machine 1 = Careful
M2 = Machine 2 = Quicky
Bad = Defective
P(M1) = 0.4
P(M2) = 0.6
P(Bad | M1) = 0.04
P(Bad | M2) = 0.10
P(M1 and Bad) = P(M1) P(Bad | M1) = ?
P(M2 and Bad) = P(M2) P(Bad | M2) = ?
P(Bad) = P(M1 and Bad) + P(M2 and Bad) = ?
P(M2 | Bad) = P(M2 and Bad) / P(Bad) = ?
```
# DDDD

Write R code to calculate `P(M2 | Bad)`.

```{r dddd}
pM1 = 0.4
pM2 = 0.6
pBadGivenM1 = 0.04
pBadGivenM2 = 0.10
pBad = (pM1 * pBadGivenM1) + (pM2 * pBadGivenM2)
pM2Bad = (pM2 * pBadGivenM2) / pBad
pM2Bad
```