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Random Variables

Probability Under the Curve of the Standard Normal Distribution

Upload speed are measured on a standard scale I which the target value is 1.0. Data collected over the past year indicate that the upload speeds are approximately normally distributed with a means of 1.005 and a standard deviation of 0.10. Each day at 25 random times , the upload speed is measured . Assuming that the distribu

Calculate Probability

Probability- in Late 2007, it was reported that 79 percent of US adults owned a cell phone. Suppose that by the end of 2010, that percentage was 85 percent. If a sample of 10 adults is selected What is the probability that a.) 8 owned a cell phone b.) At least 8 own a cell phone c.) All 10 own a cell phone D)If you sele

Applying the Concept of the Binomial Distribution

A student is taking a multiple choice exam in which each question has four choices . Assume that the student has knowledge of a correct answer to any of the questions. She has to decide on a strategy in which she will place four balls (marked A,B,C and D) into a box. She randomly selects one ball for each question and replaces t

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

Steps on calculating conditional probability

Does it take more to be removed from an email list than it used to take? A study of 100 large online retailers revealed the following? Need Three or More Clicks to be removed years yes No total 2009 39 61 100 2008 7 93 100 A. Given that three or more clicks are needed to removed from an email list, what the probability that

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

Sampling Distribution for Proportion

Question 1 After hearing of the national results that 44% of students engage in binge drinking (5 drinks ata a sitting for men, 4 for women), a professor surveyed a random sample of 244 students at his college and found that 96 of them admitted to binge drinking in the past week. Should he be surprized at this result? Explain.

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

Probability theory: minimizing expectation

Let X and Y be two random variables with E(Y)=u and EY^2 < infinity. a) show that the constant c that minimizes E(Y-c)^2 is c=u b) deduce that the random variable f(X) that minimizes E[(Y-f(X))^2|X] is f(X)=E[Y|X] c) deduce that the random variable f(X) that minimizes E(Y-f(X))^2 is also f(X)=E[Y|X]

Compute value of the expressions

Suppose that X, Y and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose also that E(X)=5 E(Y)=-6 E(Z)=-8 Var(X)=31 Var(Y)=14 Var(Z)=2 Compute the values of the expressions below. See attached

Sequence of discrete random variables: Example problem

Please see attached file for full problem. The sequence of discrete random variables Xn, with mass functions fn, is said to converge in total variation to X with mass function f if Suppose that Xn -> X in total variation and u : R -> R is bounded. Show that

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

Statistically Independent Random Variables

Two statistically random variables, X and Y, have variances of 9 and 25 respectively. Two new random variables are defined by U=3X+4Y V=5X-2Y A) Find the variances of U and V. B) Find the correlation coefficient of U and V.

identifying continuous random variable

Which of the following is a continuous random variable? a. Number of Honda Civics sold in a given day at a car dealership. b. Gallons of gasoline used for a 200-mile trip in a Honda Civic. c. Miles driven on a particular Thursday by the owner of a Honda Civic.

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

Mathematical Expectation Estimators

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

Expectation

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

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