Every day you buy a lottery ticket for $1 and there is a prize draw every day. The probability that youwin any money on the lottery is 0.0006. Let's say for simplicity that there is only one prize and that itis worth $1000.(a) Let Y be the number of days until you win a prize on the lottery. What kind of distribution doesY follow? What would be its expected value and variance? Don't round your answers.(b) You keep playing the lottery every day until you win. When you finally win the lottery and youreceive the $1000 prize will you have any profit? What will be the variance of this profit?You only start off with $300. What is the probability that you lose all of your money before youwin the lottery? Round your answer to 3 decimal places. (d) Assume that you have an unlimited amount of funds and that you can purchase an infinite numberof lottery tickets on any given day for an infinite number of draws (i.e. there is more than 1 chancea day to win the lottery), and the rate at which you win on any ticket is 0.05 per day. Let X be thenumber of times that you win the lottery on a given day - noting that we are counting somethingthat has an unlimited range and a constant rate of a win.What is the distribution of X?(e) 1) What is the expected number of times you win the lottery in a given day?2) What is the variance of the number of times that you win the lottery in a given day? Round to3 decimal places.

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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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You are playing a game at a carnival. It costs nothing to play. You can win $5 with probability 0.15 on each round, but if you lose, you pay $2. (a) Let X be the number of times it takes for you to get your first win. What distribution does X follow, and what are the expection and variance of X? (b) If you play until you win once, what is your expected net profit (positive for profit, negative for loss)? What is the variance? (c) You start with $20. What is the probability that you lose all of your money without winning even once?
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An automotive center keeps track of customer complaints received each week. The probability distributions of complaints are shown below. The random variable, xi, represents the number of complaints, and p(xi) is the probability of receiving xi complaints for two of the stores. The cost impact of each complaint is believed to be y=$10x3 where x is the number of complaints. Store A xi 0 1 2 3 4 5 6 p(xi) 0.10 0.15 0.20 0.25 0.15 0.10 0.05 Store B xi 0 1 2 3 4 5 6 p(xi) 0.10 0.15 0.25 0.22 0.13 0.08 0.07 Compute the simulated averages and standard deviations of the number of complaints per week for each store and the total for both stores over the 52 weeks. Compare to the theoretical mean and standard deviations.
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The average amount of snow per season in Trafford is 45 inches. The standard deviation is 5 inches. Use a graphing calculator to find the probability that next year Trafford will receive the given amount of snowfall. Assume the random variable is normally distributed. Round your answers to 3 decimal places. Part: 0/2 Part 1 of 2 (a) Find the probability Trafford will receive at most 54 inches of snow. The probability that Trafford will receive at most 54 inches of snow is X
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Summer Wine Sales 1000 2000 3000 4000 5000 0000 7000 Assume that the weekly summer wine sales at the local winery vary with a mean of u 2600 dollars and standard deviation o= 1300 dollars. The student is actually going to attend a wedding at the winery in August, and he is wondering what is the probability that the sales for that week will be more than 2500 dollars. Can he calculate this probability? O Yes O No
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