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), ...

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), ...

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 ...

We obtain a closed form expression for the joint probability mass function of the occupation times for a Three-State Markov chain. Our representation extends the long-standing result for a Two-State ...

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 ...

Will Kenton is an expert on the economy and investing laws and regulations. He previously held senior editorial roles at Investopedia and Kapitall Wire and holds a MA in Economics from The New School ...

Abstract: Among ultrasound images, the acoustic radiation force impulse (ARFI) image can provide information about the stiffness of the tissue using both a pushing beam and a detection beam. However, ...

Abstract: Sunlight throughout urban areas largely impacts local climate [sustainable development goal (SDG) 13], residents’ well-being (SDG 3), and access to clean energy (SDG 7). However, sunlight ...