Monthly Archives: September 2016

A problem asks the following. Let be independent random variables where are identically distributed and takes values . Show that if then The first two follow due to being idependenty and identically distributed The last two we compute by using … Continue reading →

A problem asks the following. The conditional variance of with respect to is the random variable where is a decomposition of the sample space. Show that We can read this as the follows. The variance of is the sum of … Continue reading →

Going with the theme of trying to transplant probability laws to expectations consider the following. if are independent events we know that . Now, if are independent random variables then A question now asks to give an example of random … Continue reading →

Sometimes expectations and random variables appear in so many ways that I find it a little confusing at times. The book I am following has a neat diagram that helps quite a bit. Expectations Basic Expectation Start with a distribution … Continue reading →

In the coin tossing setup, we saw that the fraction of observed heads in trails approaches as . The function is called an estimator that takes on a value in . It’s a special kind of estimator called an unbiased … Continue reading →

Problem 6.2 asks the following. Let be a nonnegative even function that is nondecreasing for positive . Then for a random variable with , From the looks of it, the upper bound seems simple enough because it looks like a … Continue reading →

Suppose I tell you the axioms of elementary probability and suppose further that I tell you that I have a coin that, on tossing, will show Heads with a probability of . Can you tell anything at all abou the … Continue reading →