Question

# Poisson Distribution: p(x, λ)  =   λx  exp(-λ) /x!  ,  x = 0, 1, 2, ….. Find the moment generating function Mx(t)...

1. Poisson Distribution: p(x, λ)  =   λx  exp(-λ) /x!  ,  x = 0, 1, 2, …..

1. Find the moment generating function Mx(t)

1. Find E(X) using the moment generating function

2. If X1 , X2 , X3  are independent and have means 4, 9, and 3, and variencesn3, 7, and 5. Given that Y = 2X1  -  3X2  + 4X3. find the

1. mean of Y
2. variance of  Y.

3. A safety engineer claims that 2 in 12 automobile accidents are due to driver fatigue. Using the formula for Binomial Distribution find the probability that at least 3 of 5 automobile accidents are due to driver fatigue.

4. The number of complaints that a dry-cleaning establishment receives per day is a random variable having   Poisson distribution with λ = 1.8.  Use Poisson distribution formula to find the probability that there will be at most  two complaints on any given day.

5.

i. Define Geometric distribution.

1. Show that it is a distribution

1. Find the moment generating function for Geometric distribution

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