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Correct 5th problem url #28

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Correct 5th problem url #28

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8 changes: 4 additions & 4 deletions manuscript/04_expectations.md
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Original file line number Diff line number Diff line change
Expand Up @@ -75,7 +75,7 @@ myHist <- function(mu){
binwidth=1, aes(y = ..density..), color = "black")
g <- g + geom_density(size = 2)
g <- g + geom_vline(xintercept = mu, size = 2)
mse <- round(mean((galton$child - mu)^2), 3)
mse <- round(mean((galton$child - mu)^2), 3)
g <- g + labs(title = paste('mu = ', mu, ' MSE = ', mse))
g
}
Expand Down Expand Up @@ -159,7 +159,7 @@ trying to find the point where it balances out.
### Example

Consider a density where {$$}f(x) = 1{/$$} for {$$}x{/$$} between zero and one.
Suppose that {$$}X{/$$} follows this density; what is its expected value?
Suppose that {$$}X{/$$} follows this density; what is its expected value?

![Uniform Density](images/uniform.png)

Expand Down Expand Up @@ -244,12 +244,12 @@ are centered around 0.5.
- The more data that goes into the sample mean, the more.
concentrated its density / mass function is around the population mean.

## Exercises
## Exercises

1. A standard die takes the values 1, 2, 3, 4, 5, 6 with equal probability. What is the expected value?
2. Consider a density that is uniform from -1 to 1. (I.e. has height equal to 1/2 and looks like a box starting at -1 and ending at 1). What is the mean of this distribution?
3. If a population has mean {$$}\mu{/$$}, what is the mean of the distribution of averages of 20 observations from this distribution?
4. You are playing a game with a friend where you flip a coin and if it comes up heads you give her {$$}X{/$$} dollars and if it comes up tails she gives you $Y$ dollars. The odds that the coin is heads is {$$}d{/$$}. What is your expected earnings? [Watch a video of the solution to this problem](http://youtu.be/5J88Zq0q81o?list=PLpl-gQkQivXhHOcVeU3bSJg78zaDYbP9L) and [look at the problem and the solution here.](http://bcaffo.github.io/courses/06_StatisticalInference/homework/hw1.html#5).
5. If you roll ten standard dice, take their average, then repeat this process over and over and construct a histogram what would it be centered at?
[Watch a video solution here](https://www.youtube.com/watch?v=ia3n2URiJaw&index=16&list=PLpl-gQkQivXhHOcVeU3bSJg78zaDYbP9L)
and [see the original problem here](http://bcaffo.github.io/courses/06_StatisticalInference/homework/hw2.html#11).
and [see the original problem here](http://bcaffo.github.io/courses/06_StatisticalInference/homework/hw2.html#10).