From b6ef886e1e32a00afa606f0f32d8362f9be5d239 Mon Sep 17 00:00:00 2001 From: Kostas Giannakakis Date: Mon, 28 Sep 2015 18:33:04 +0300 Subject: [PATCH] Correct 5th problem url --- manuscript/04_expectations.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/manuscript/04_expectations.md b/manuscript/04_expectations.md index 9a38f4d..7b9549e 100644 --- a/manuscript/04_expectations.md +++ b/manuscript/04_expectations.md @@ -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 } @@ -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) @@ -244,7 +244,7 @@ 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? @@ -252,4 +252,4 @@ concentrated its density / mass function is around the population mean. 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).