
Recent Posts
Recent Comments
Archives
Categories
Meta
Monthly Archives: September 2016
Reification And Reflection In Haskell (20/365)
I am reading the paper Functional Pearl: Implicit Configurations and I will go on to see how to use the hackage library reflection based on this paper which allows one to pass around configuration data in an elegant manner. Before … Continue reading
Conditional Probability – Problem (19/365)
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
Conditional Probability – Problem (18/365)
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
Conditional Probability – Problem (17/365)
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
Expectations (16/365)
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
Unbiased Estimator (15/365)
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
More Time Utilities (14/365)
In the previous post I introduced a basic datetime type and said that I’ll provide a DSL to do much more with it. Here is a datetime matching DSL I will support. data Match = DowMatch (UArray Int Bool)  … Continue reading
More Time Utilities (13/365)
Suppose you want to add one second to the current date. One approach is to convert it to unixtime (seconds from epoch), add , and then convert it back. The cost of converting is a little too high if we … Continue reading
Chebyshev’s Inequality For Bounding From Below? (12/365)
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
What’s Real About Probability? (11/365)
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