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 ...

(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 ...

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 ...

A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes ...

Abstract: A novel location estimation with Maximum Log-Likelihood Function using joint probability function (PDF) of Received Signals and prior Measured Signals is proposed in order to improve the ...

The fundamental problem considered is that of the existence of a joint probability distribution for momentum and position at a given instant. The philosophical interest of this problem is that for the ...