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Random Variables

Finding Probability

7. Row 26 of the excel file gives the number of employed persons having a specific education level. a. Find he probability that an employed person has attained each of the educational levels listed in the data. b. suppose that A is the event "has at least an Associates Degree" and B is he event " is at least a high school gr

Probability and Statistics

1. As an alternative to flextime, many companies allow employees to do some of their work at home. Individuals in a random sample of 300 workers were classified according to salary and number of workdays per week spent at home. The results of are given in the table. Is there sufficient evidence to indicate that family income

Testing of Variance with Chi-Square

Hybrid Vehicle Gas Mileage. An automotive manufacturer believes that the variance of the gas mileage for its hybrid vehicles is 7.5. You work for an energy conservation agency and want to test this claim. You find that a random sample of the miles per gallon of 25 of the manufacturer's hybrid vehicles has a variance of 8.0. Let

Probability utility function and decision trees

Pierre has a utility function for total asset position of u(x)=ln(x), His assets currently consist of $50,000 in cash and a rare violin he inherited from a rich uncle which is valued at $100,000. He is debating whether to buy insurance for the violin at an annual premium, Pr. There is a 1% chance that his violin will be lost, da

What is an experiment

Twenty accounting students are randomly assigned to two different sections of an intermediate accounting class. Each section ends up consisting of 10 students. In one of the sections, computer-assisted instruction and review software is utilized; in the other section, it is not. All students are given the same final examination

Describe a discrete random variable, a Bernoulli experiment

Part A: A random variable is a numerical value determined by the outcome of an experiment. Briefly describe a discrete random variable. For each of the following indicate whether the random variable is discrete, and provide your reasoning. i) The distance between Gainesville, Florida, and all Florida cities

Linear Functions of Random Variables

X and Y are independent, normal random variables with E(X)=0, V(X)=4, E(Y)=10, V(Y)=9. Determine the following: a) P(2X + 3Y) b) V(2X + 3Y) c)P(2X +3Y<30) d)P(2X + 3Y<40)

continuous random variables

Which of the following are continuous random variables? I. the weight of an elephant II. the time to answer a questionnaire III. the number of floors in a skyscraper


I am having trouble with some estimators. I have defined a random variable Z such that Z=Y/X, where X and Y are random variables. I know that E(Y given X)=theta*X, where theta is an unknown parameter. I have worked out that E(Z)=theta. Now I am having trouble with an estimator defined as W=Ybar/Xbar, where Ybar and Xbar refer


A doctor advices a patient to go on a particular diet for 2 weeks. Considering the general condition of the patient, the amount of weight the patient may loose is assumed to be between 5 Kg and 10 Kg, and all the amounts are felt equally likely. Find the expected lose of weight

Distributions of two random variables

Please show all steps so that I can get an understanding of how the answer was derived. (See attached file for full problem description with proper equations) Problem 1 Let f(x , y)=3/2, x be the joint p.d.f. of X and Y. Find (a) P(0) (b) P(1/2) (c) P(1/2) (d) P(X) (e) Are X and Y independent?

Random variable

Suppose that are continuous with joint pdf f( )= if and zero otherwise. Derive the joint Moment Generating Function.

Characteristic functions

I am having trouble with a few characteristic functions, as described in the attachment. Any help would be greatly appreciated. The attachment contains a definition of what I mean by a characteristic function. Thank you!

St Petersburg Paradox - Random variables

This is a two part problem that expands on the St Petersburg Paradox. I have attempted this problem and ca not seem to arrive at the answers given in my book. (a) c/2-c (b) 2 log2 Below is the problem A fair coin is flipped until the first tail appears; we win $2 if it appears on the first toss, $4 on the second and in gen