Detailed solution please Detailed solution please 3 Let X be

Detailed solution please

Detailed solution please 3. Let X be the number showing when a die is thrown. Find the density function for Y = (X - 3)^2. Bonus. Assume everyone in a population of size n buys one lottery ticket each week. Use these hints to find the probability someone will win twice before you win once. (a) Let X be the event that you win in week X and nobody has won twice. Find P(X = k), k =1 2,3... n. (b) Show the probability you win once before someone else wins twice is 1/n + 1(1 + 1/n)^n. (C) What happens to (1 +1/n)^n as n right arrow infinite? What can you conclude about the lottery?

Solution

Probability for X=1/6 (for any number)

Y=(X-3)^2

1/6-3=-17/18

(-17/18)^2

Y=289/324

Y=0.89