Statistics and probability distributions
Include the intermediate steps of your calculation.

Find the following values by using the Poisson tables in Appendix A.

a. P (x = 6|lamda = 3.8)
b. P (x > 7|lamda = 2.9)
c. P (3 <= x <= 9|lamda = 4.2)
d. P (x = 0|lamda = 1.9)
e. P (x <= 6|lamda = 2.9)
f. P (5 < x <= 8|lamda = 5.7)

5.20. According to the United National Environmental Program and World Health Organization, in Mumbai, India, air pollution standards for particulate matter are exceeded an average of 5.6 days in every three-week period. Assume that the distribution of number of days exceeding the standards per three-week period is Poisson distributed.

a. What is the probability that the standard is not exceeded on any day during a three-week period?

b. What is the probability that the standard is exceeded exactly six days of a three-week period?

c. What is the probability that the standard is exceeded 15 or more days during a three-week period?
If this outcome actually occurred, what might you conclude?

6.2. x is uniformly distributed over a range of values from 8 to 21.

a. What is the value of f (x) for this distribution?
b. Determine the mean and standard deviation of this distribution.
c. Probability of (10 less than or equal to x which is less than 17)
d. Probability of (x is less than 22)??
e. Probability of (x is greater than or equal to 7)?

Solution Summary

The solution provides step by step method for the calculation of Poisson and uniform probabilities. Formula for the calculation and Interpretations of the results are also included.

Please use words to describe the solution, not just symbols. (basically, explain what is going on in addition to an answer) Use a math symbol editor where appropriate.
Problem 1:
Write a program to compute binomial probabilities and compare the results with the Poisson approximation for the following cases:
a) P(X = 2)

The Poisson distribution is given by the following
P(x,λ)=e ^ -λ * λ^x! x=0,1,2,3.....j.....
Where λ>0 is a parameter which is the average value μ in poisson distribution.
a) show that the maximum poisson probability P(x=j,λ) occurs at approximately the average value, that is λ=j if λ>1.
(hint: you can take t

Objective: Calculate binomial and Poissonprobabilities.
1) Chapter 5: Problem 5.5 (binomial)
Solve the following problems by using the binomial formula.
a. If n = 4 and p = .10 , find P(x = 3) .
b. If n = 7 and p = .80 , find P(x = 4) .
c. If n = 10 and p = .60 , find P(x ≥ 7) .
d. If n = 12 and p = .45

You arrive at a bus stop at 10 o'clock, knowing that the bus will arrive at some time uniformly distributed between 10:00 and 11:00.
a) What is the probability that you will have to wait longer than 10 minutes?
b) If at 10:20 the bus has not arrived, what is the probability that you will have to wait atleast an additional 10 m

Use the Poisson Distribution the indicated probabilities in one year, there were 116 homicide deaths in Richmond VA. For a randomly selected day, find the probability that the number of homicide deaths is 1.

Use the Poisson distribution to find the indicated probabilities. Currently, 11 babies are born in the village of West point, population of 760, each year. Find the probability that on a given day, there is at least one birth.

Let X have a Poisson distribution with a mean of 4. Find
a) P(23)
c) P(X<3)
Let X have a Poisson distribution with a variance of 4. Find P(X=2)
Customers arrive at a travel agency at a mean rate of 11 per hour. Assuming that the number of arrivals per hour has a Poisson distribution, give the probability th

Patients arrive at the emergency room of Costa Valley Hospital at an average of 5 per day. The demand for emergency room treatment at Costa Valley follows a Poisson distribution.
a. Using appendix C, compute the probability of exactly 0,1,2,3,4 and 5 arrivals per day.
b. What is the sum of these probabilities and why is th

During the period of time that a local university takes phone-in registrations, calls come in at the rate of one every two minutes. [Hint: It is a Poisson Distribution Problem.]
a) What is the expected number of calls per hour?
b) What is the probability of three calls in five minutes?
c) What is the proba