Question

# 1. Given a poisson random variable, X = # of events that occur, where the average...

1. Given a poisson random variable, X = # of events that occur, where the average number of events in the sample unit (μ) is given on the right, determine the smallest critical value (critical value = c) for the random variable such that you have at least a 99% probability of finding c or fewer events.
μ = 4

2. Given a binomial random variable X where X = # of operations in a local hospital that result in an infection for a random sample of n patients. Calculate the standard deviation of the number of infections where the probability of an infection is p (given on right). n=8 , p=0.1

3. Asssume the number of accidents that occur on campus each week during the semester is a poisson random variable where the average number of accidents each week (μ) is given on the right. Calculate the probability that the number of accidents next week is between "a" and "b" (including "a" and "b").

 μ =0.5 , a=1 ,b=3
 4 . Asssume the number of accidents that occur on campus each week during the semester is a poisson random variable where the average number of accidents each week (μ) is given on the bottom. Calculate the probability that the number of accidents next week is equal to "a" [ P(X=a) ], given on the bottom. μ = 0.5 , a=1

1) Since so PMF is

Then by given condition we get

Put c=9 gives

Thus the required value of c is 9

2) The standard deviation of binomial distribution is

Use the given values we get

3) Required probability is

4) Required probability is