Derive the MGF of Cauchy’s distribution.

2. What make the Chi square distribution a special case of the Gamma Distribution?

Compare and contrast the three distributions, uniform normal and exponential, particular in reference to the calculus behind them

A medical company pack medication in bags marked as 250 gA large number of packs of medication were weighed and the mean and standard deviation were calculated as 255 g and 2.5 g respectively.Assuming this data is normally distributed, what percentage of packs are underweight? Develop a Standard Normal Distribution curve.

Need only handwritten solution only (not typed one).

A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by the following distribution: X~ Exp(0.2) What type of distribution is this?

Suppose that the City of Chicago is interested in potential revenues if they introduce a tolling station near O'Hare. Further suppose that the average time between cars is only 3.0 seconds; what is the average value of the distribution?

5.24 Grades in a math course. Indiana University posts the grade distributions for its courses online." In one spring semester, students in Math 118 received 16.1% A's, 34.3% B's, 29.2% C's, 9.6% D's, and 9.8% F's. 11 (a) Using the common scale A = 4, B = 3, C = 2, D = 1, F = 0, take X to be the grade of a randomly chosen Math 118 student. Use the definitions of the mean (page 237) and standard deviation (page 245) for discrete random variables to find the mean µ and the standard deviation o of grades in this section. %3D

Under what conditions will you use the Poisson and Binomial distributions?