What are the mean and standard deviation of a probability

Addison Gross

Addison Gross

Answered question

2022-01-30

What are the mean and standard deviation of a probability density function given by Pr(X=k)=12ke12k! for k{0,1,2...}?

Answer & Explanation

fionaluvsyou0x

fionaluvsyou0x

Beginner2022-01-31Added 11 answers

Explanation:
Probability of events for a Poisson distribution
An event can occur 0, 1, 2, … times in an interval. The average number of events in an interval is designated λ . λ is the event rate, also called the rate parameter. The probability of observing k events in an interval is given by the equation
P(k events in interval)=λkeλk!
The mean is equal to the variance
mean=λ=σ2
and standard deviation σ=λ
mean λ=12
standard deviation λ=12=3.464

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