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)?
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.