13) Suppose that a die is rolled twice. Let X be the maximum value to appear in the two rolls. Find the pmf of X. Find E[X].
13) Suppose that a die is rolled twice. Let X be the maximum value to appear...
A fair tetrahedron (four-sided die) is rolled twice. Let X be the random variable denoting the total number of dots in the outcomes, and Y be the random variable denoting the maximum in the two outcomes. Thus if the outcome is a (2, 3) then X = 5 while Y = 3. (a) What are the ranges of X and Y ? (b) Find the probability mass function (PMF) of X and present it graphically. Describe the shape of this...
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 6-sided die rolled twice. Let E E be the event "the first roll is a 2" and F F the event "the second roll is a 2". (a) Are the events E and F independent? Yes or No: (b) Find the probability of showing a 2 on both rolls. Write your answer as a reduced fraction.
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 6-sided die rolled twice. Let E be the event "the first roll is a 5" and F F the event "the second roll is a 5". (a) Are the events E E and F F independent? Input Yes or No: (b) Find the probability of showing a 5 on both rolls. Write your answer as a reduced fraction. Answer:
A tetrahedron (four-sided die) is rolled twice and the sum X of k is the results of the two rolls is recorded. We know that the chance that X proportional to k. (a) What is the probability model for X, i.e., uhat values can X take, and what are the corresponding probabilities? (b) Compute the chance that the sum of the two rolls will erceed but ill not be more than b (c) Compute the erpected value of x.
Suppose a fair die is rolled 10 times. Find the numerical values of the expectations of each of the following random variables: a). the sum of the numbers in the 10 rolls; b). the sum of the largest 2 numbers in the first 3 rolls; c). the maximum number in the first 5 rolls; d). the number of multiples of 3 in the 10 rolls; e). the number of faces which fail to appear in the 10 rolls; f). the...
A die is rolled twice. Let X1 and x2 be the outcomes, and let s= X1 + x2 be the sum of these outcomes. 1. What is the expected value of x1 and x2? 2. What is the standard deviation of x1 and x2? 3. What is the expected value and standard deviation of sA die is rolled twice. Let X1 and x2 be the outcomes, and let s= X1 + x2 be the sum of these outcomes. 1. What...
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
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