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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
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
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