by Rahul Anand | Jul 19, 2023 | PROBABILITY
In probability theory and statistics, λ (lambda) is a parameter that represents the average rate or average number of events occurring in a fixed interval in a Poisson distribution. In the context of the Poisson distribution, λ determines the shape and characteristics...
by Rahul Anand | Jul 19, 2023 | PROBABILITY
Computation of the Second Moment of Poisson Distribution or in other words, Prove that for Poisson Distribution, the second moment is given by \( E(X^2) = λ(λ+1) \) For Poisson Distribution, we have \( P(X=k) = λ^{k} . \dfrac{e^{-λ}}{k!} \) for k = 0,1,2,… We...
by Rahul Anand | Jul 14, 2023 | PROBABILITY
As a professional in the field of mathematics and statistics, I am often asked to explain the concept of probability theory and random variables. Probability theory is a branch of mathematics that deals with the analysis of random phenomena, while random variables are...
by Rahul Anand | Jul 13, 2023 | PROBABILITY
Some practical examples of continuous random variables: The height of a person. The height of a person can take on any value between the minimum and maximum height possible for a human. There are an infinite number of possible heights, so height is a continuous...
by Rahul Anand | May 9, 2023 | PROBABILITY
Question What does it mean for one event 𝐶 to cause another event 𝐸 – for example, smoking (𝐶) to cause cancer (𝐸)? There is a long history in philosophy, statistics, and the sciences of trying to clearly analyze the concept of a cause. One tradition says that...
by Rahul Anand | May 9, 2023 | PROBABILITY
Solution We have A = (1,4), (2,3), (3,2), (4,1) B = (1,4), (2,4), (3,4), (4,4), (5,4), (6,4), (4,1), (4,2), (4,3), (4,5), (4,6) \( P(A|B) = \dfrac {P(A∩B)}{P(B)} \) \( A∩B = (1,4), (4,1) \) The sample space comprises of 6×6 = 36 eventsHence,\( P(A∩B) = \dfrac{2}{36} =...
