by Rahul Anand | Jul 19, 2023 | PROBABILITY
Derive the Mean or Expected Value of Random Variable that has Poisson Distribution or Prove that for Poisson Distribution, \( μ = E(X) = λ \) We have \( P(X=k) = λ^{k} . \dfrac{e^{-λ}}{k!} \) for k = 0,1,2,… We now derive the Expected Value(μ) of Poisson Distribution...
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 12, 2023 | TRIGONOMETRY
The six trigonometric functions are defined below. Refer to the above diagram to get the relational picture. sinθ = \( \dfrac {\mathrm{perpendicular}} {\mathrm{hypotenuse}} = \dfrac {p}{h} \) cosθ = \( \dfrac {\mathrm{base}} {\mathrm{hypotenuse}} = \dfrac {b}{h}...
