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If a random variable x satisfies the Poisson’s distribution with a mean value of 3, then the probability that (x ≥ 2) is Poisson’s distribution,
Correct answer is between '0.79,0.82'. Can you explain this answer?
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Distribution with parameter λ, we write x ~ Poisson(λ). The probability mass function (pmf) of x is given by:
P(x=k) = (λ^k * e^(-λ)) / k!
where k is a non-negative integer (i.e. k=0,1,2,...) and e is the mathematical constant approximately equal to 2.71828.
The parameter λ represents the average number of occurrences of an event in a given time or space interval. For example, if we are interested in the number of customers arriving at a store per hour, λ would represent the average number of customers per hour.
The Poisson distribution has several important properties:
1. The mean and variance of x are both equal to λ.
2. The Poisson distribution is a limiting case of the binomial distribution, when the number of trials n becomes very large and the probability of success p becomes very small, while the product np remains constant.
3. The Poisson distribution is often used to model rare events, such as the number of accidents per day in a city or the number of defects in a manufacturing process.
4. The Poisson distribution is also used in queuing theory, where it models the arrival and service times of customers in a system.
Overall, the Poisson distribution is a useful tool for modeling discrete random variables that represent counts or rates of events, and it has many practical applications in various fields of science and engineering.
P(x=k) = (λ^k * e^(-λ)) / k!
where k is a non-negative integer (i.e. k=0,1,2,...) and e is the mathematical constant approximately equal to 2.71828.
The parameter λ represents the average number of occurrences of an event in a given time or space interval. For example, if we are interested in the number of customers arriving at a store per hour, λ would represent the average number of customers per hour.
The Poisson distribution has several important properties:
1. The mean and variance of x are both equal to λ.
2. The Poisson distribution is a limiting case of the binomial distribution, when the number of trials n becomes very large and the probability of success p becomes very small, while the product np remains constant.
3. The Poisson distribution is often used to model rare events, such as the number of accidents per day in a city or the number of defects in a manufacturing process.
4. The Poisson distribution is also used in queuing theory, where it models the arrival and service times of customers in a system.
Overall, the Poisson distribution is a useful tool for modeling discrete random variables that represent counts or rates of events, and it has many practical applications in various fields of science and engineering.
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If a random variable x satisfies the Poisson’s distribution with a mean value of 3, then the probability that (x ≥ 2) isPoisson’s distribution,Correct answer is between '0.79,0.82'. Can you explain this answer?
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