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STAT 202: Individual Assignment x>0 1. Given the Gamma distribution as ƒ(x) = { 10 elsewhere Find the mean and variance of the distribution.

STAT 202: Individual Assignment x>0 1. Given the Gamma distribution as ƒ(x) = { 10 elsewhere Find the mean and variance of the distribution.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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STAT 202: Individual Assignment x>0 1. Given the Gamma distribution as f(x) =- elsewhere Find the mean and variance of the distribution. 2a. Suppose that a large conference room for a certain hotel can be reserved for no more than 4 hours. However, the use of the conference room is such that both long and short conferences occur quite often. In fact, it can be assumed that length X of a conference has a uniform distribution on the interval [0, 4]. i. Determine the probability density function ii. What is the probability that any given conference last at least 3 hours? b. A cement wholesale distributor has a large store that hold fixed supplies and are filled every Sunday. Of interest to the wholesaler is the proportion of this supply that is sold during the week. Over many weeks of observation, the distributor found out that this proportion could be modeled by a beta distribution with a = 4 and ß = 2 . Find the probability that the wholesaler will sell at least 90% of his stock in a given week. 3. A random variable X has the density function given by; x20 f(x) = Find the Moment generating function. otherwise [3x, 4a. Given the pdf f (x) = { 0<x<l elsewhere and Y = 2X +1
Transcribed Image Text:STAT 202: Individual Assignment x>0 1. Given the Gamma distribution as f(x) =- elsewhere Find the mean and variance of the distribution. 2a. Suppose that a large conference room for a certain hotel can be reserved for no more than 4 hours. However, the use of the conference room is such that both long and short conferences occur quite often. In fact, it can be assumed that length X of a conference has a uniform distribution on the interval [0, 4]. i. Determine the probability density function ii. What is the probability that any given conference last at least 3 hours? b. A cement wholesale distributor has a large store that hold fixed supplies and are filled every Sunday. Of interest to the wholesaler is the proportion of this supply that is sold during the week. Over many weeks of observation, the distributor found out that this proportion could be modeled by a beta distribution with a = 4 and ß = 2 . Find the probability that the wholesaler will sell at least 90% of his stock in a given week. 3. A random variable X has the density function given by; x20 f(x) = Find the Moment generating function. otherwise [3x, 4a. Given the pdf f (x) = { 0<x<l elsewhere and Y = 2X +1
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