4. A pair of fair dice is rolled. Let X be the largest of the number...
(20pts) Problem 3. A pair of fair dice are cast, and the number of rolled dots, on each die, is recorded. Let X denote the difference of the two numbers (10pts)a. Find the probability mass function of X. b. Find the expected value E(X).
Shandelle rolls a pair of fair dice and sums the number of spots that appear on the up faces. She then flips a fair coin the number times associated with the sum of the spots. For example, if she rolled a 3 and a 4, then she flips the fair coin 7 times. If the coin flipping part of the random experiment yielded an equal number of heads and tails, find the probability that she rolled an 8 on the...
suppose ana has a pair of dice. Let X= the difference of the largest minus the smallest number of showing on the dice. Find the PMF for X.
A pair of fair dice is rolled. What is the probability of each of the following? (Round your answers to three decimal places.) (a) the sum of the numbers shown uppermost is less than 5and (b)at least one 5 is cast
Consider a roll of a pair of fair dice. Let X = absolute value of the difference of the two dice. What are the possible values that X can take on? Derive both the mass function and the distribution function for X.
Let X equal the larger outcome when a pair of 6-sided dice are rolled.(a) Assuming the two dice are independent, show that the probability function of \(X\) is \(f(x)=\frac{2 x-1}{36} \quad x=1, \ldots, 6\)(b) Confirm that \(f(x)\) is a probability function.(c) Find the mean of \(X\).(d) Can you generalise \(E(X)\) to a pair of fair \(m\) -sided dice?\(\left[\right.\) Hint: recall that \(\sum_{i=1}^{n} i=n(n+1) / 2\) and \(\left.\sum_{i=1}^{n} i^{2}=n(n+1)(2 n+1) / 6\right]\)
3. If a pair of dice is rolled 4 times (i.e., each die is rolled 4 times) and the sum of the dice is always less than or equal to 6, should we feel confident that the dice are not fair? 4. Repeat problem 3 if the pairs of dice are rolled 6 times instead of 4 times.
A fair pair of dice is rolled 36 times. Find the probability that the same point comes up on both dice at least 11 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...
Two identical fair 6-sided dice are rolled simultaneously. Each die that shows a number less than or equal to 4 is rolled once again. Let X be the number of dice that show a number less than or equal to 4 on the first roll, and let Y be the total number of dice that show a number greater than 4 at the end. (a) Find the joint PMF of X and Y . (Show your final answer in a...