(i) check that it is a joint density function or not? (Use integral2()) (ii) find marginal distribution g(x) at x = 1. (iii) find the marginal distribution h(y) at y = 0. (iv) find the expected value ...

We toss an unbiased coin four times, and choose \(\Omega=\{H,T\}^4\) for our sample space. We write \(X\) for the number of heads in the first three tosses and \(Y\) for the number of heads in the ...

In this lesson, you'll look at a way to represent discrete distributions - the probability mass function (PMF), which maps from each value to its probability. A probability mass function (PMF), ...

The joint probability density function \(f\) of two random variables \(X\) and \(Y\) satisfies, for every \(a_1 b_1\) and \(a_2 b_2\), \[ P(a_1\le X\le b_1, a_2\le Y ...