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Suppose a fair die is rolled 15 times. Let x be the number of faces that never show up in these 15 rolls.
7. In n rolls of a fair die, let X be the number of times 1 is rolled, and Y the number of times 2 is rolled. Find the conditional distribution of X given Y-m 7. In n rolls of a fair die, let X be the number of times 1 is rolled, and Y the number of times 2 is rolled. Find the conditional distribution of X given Y-m
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)
a player rolls a pair of fair die 10 times. the number X of 7's rolled is recorded
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)
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.
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.
A die is rolled 20 times. Given that three of the rolls came up number 1, five came up number 2, four came up number 3, two came up number 4, three came up number 5, and three came up number 6, how many different arrangements of the outcomes are there?
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...
A fair die is rolled 12 times. What is the expected sum of the 12 rolls?