(ct) The Posson distribution is deployed by engineers for extreme events. If events happen independently af each other, with average number of events in same fixed interval 1, then the distribution of the number of events k in that interval is Poisson and takes the form : e-dak P(X = k) = k! (i) European railway statistics compiled by mechanical engineers over the past 50 years reveal that 4 train crashes cccur on average in continental europe and the UK each year. Assuming the data follows a Poisson distribution, evaluate the probability that there will be 2 crashes this year.

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A:

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A: According to the given information, we have Mean = 1000 Standard deviation = 200

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A: Given that  n= 100  And X ~ Pois (1)

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A: The time between two events follows Exponential distribution with λ=1/hour

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A: Binomial distribution is given by

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A: Given information:

Q: Suppose random variable X has a Poisson distribution with t​ = 2 and λ= 4. What is​ E(X)?

A:

Q: If a random variable X has a Poisson distribution with P(X = 1) 2P(X = 2). What is P(X = 3)? %3D 2

A: Hence,  Option (a)  e^-1/6 , is the correct✅ choice.

Q: 8 Suppose the mean income of Firms in the industry for a year is 95 million dollars with a Standard…

A: given data, μ=95 millon dollars σ=5  millon dollars normal distribution probability that a randmoly…

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Q: 45 It can be shown that if events are occurring in time according to a Poisson distribution with…

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