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 ...

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 ...

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 ...

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 ...

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, ...