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λ (lambda) in Poisson distribution

λ (lambda) in Poisson distribution

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...
Practical Examples of Continuous Random Variables

Practical Examples of Continuous Random Variables

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...

Probability Cause and Effect Problem

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...

Probability Problem: Suppose you roll a fair die two times. Let 𝐴 be the event “THE SUM OF THE THROWS EQUALS 5” and 𝐵 be the event “AT LEAST ONE OF THE THROWS IS A 4”. Solve for the probability that the sum of the throws equals 5, given that at least one of the throws is a 4. That is, solve 𝑃(𝐴|𝐵).

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} =...