7. In n rolls of a fair die, let X be the number of times 1 is rolled, and Y the number of times ...
I know Pk~1/k^5/2 just need the work Problem 1. Suppose that a fair six-sided die is rolled n times. Let N be the number of 1's rolled, N2 be the number of 2's rolled, etc, so that NN2+Ns-n Since the dice rolls are independent then the random vector < N,, ,Ne > has a multinomial distribution, which you could look up in any probability textbook or on the web. If n 6k is a multiple of 6, let Pa be...
Suppose a die is rolled six times. Let X be the total number of fours, and let Y be the number of fours in the first two rolls. Find the distribution and the expectation of X given Y.
a player rolls a pair of fair die 10 times. the number X of 7's rolled is recorded
Problem 6. A fair die is rolled four times. (a) Let Y denote the number of distinct rolls. Find the probability mass function of Y. (b) Let Z denote the minimal result fo the 4 throws. Find the probability mass function of Z
If a die is rolled six times, let X be then number the die obtained on the first roll and Y be the sum of the numbers obtained from all the rolls. Find the expected value and variance of x and y.
9. A fair die is successively rolled. Let X and Y denote, respectively, the rolls necessary to obtain a six and a fhve. Find (a) ElX), (b) E(X|Y = 1], (c) ElXlY = 5l
5. A fair six sided die is rolled 10 times. Let X be the number of times the number '6' is rolled. Find P(X2)
A fair die is rolled 100 times. Let X add the faces of all of the rolls together. Then µ = 350. Find an upper bound for P(X ≥ 400). Find the actual probability P(X = 100)
We roll a fair 8-sided die five times. (A fair 8-sided die is equally likely to be 1, 2, 3, 4, 5, 6, 7, or 8.) (a) What is the probability that at least one of the rolls is a 3? (b) Let X be the number of different values rolled. For example, if the five rolls are 2, 3, 8, 8, 7, then X = 4 (since four different values were rolled: 2,3,7,8). Find E[X].
b) Find Var(X) 5. A fair six sided die is rolled 10 times. Let X be the number of times the number '6' is rolled. Find P(X2) B SEIKI