Skip to content

Correct 5th problem url #28

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Open
kgiannakakis wants to merge 1 commit into
base: master
Choose a base branch
from
Open

Correct 5th problem url #28

Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
8 changes: 4 additions & 4 deletions manuscript/04_expectations.md
View file
Open in desktop
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).