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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