let X1 face the value of the first die,X2face the value of the 2nd die Y...
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...
(4) Consider rolling three dice. Let X1, X2, and X3 the values which appear on the three dice, respectively. Let Y be the maximum out of all three dice. (a) Find the conditional PMF py)xi (yr) (b) Find the probability that the maximum of all three dice is 4 given that the first die is a 3. (c) Find the probability that the maximum of all three dice is 3 given that the first die is a 3 (4) Consider...
(4) Consider rolling three dice. Let X1, X2, and X3 the values which appear on the three dice, respectively. Let Y be the maximum out of all three dice. (a) Find the conditional PMF py)xi (yr) (b) Find the probability that the maximum of all three dice is 4 given that the first die is a 3. (c) Find the probability that the maximum of all three dice is 3 given that the first die is a 3 (4) Consider...
3. Two fair, four-sided dice are rolled. Let X1, X2 be the outcomes of the first and second die, respectively. (a) Find the conditional distribution of X2 given that Xi + X2 = 4. (b) Find the conditional distribution of X2 given that Xi + X2-5.
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...
We roll two dice. Assume all 36 possibilities are equally likely. Let X1 and X2 be the result of the first and second die, respectively. Let S be the sum of the scores, that is S = X1 + X2. Calculate the following: (a) P(S = k), for k 2,3,... 12. (b) P(X1 = 2 S = k) for k = 2,3,... 12. (c) P(X1 = 6|S = k) for k = 2, 3, ... 12.
Question 3 Suppose an unfair die is to an unfair die is rolled. Let random variable X indicate the number that the die lands on when rolled taking on the following probability values T 1 2 X Pr(X=> 1 1 .05 1 05 2 .10 3 20 4 40 5 .15 6 .10 A) Find the probability of rolling a 2 or a 6. ilor si s lo sonensyon b el B) Find the probability of rolling a number greater...
(2) Consider rolling three dice. Let X1, X2, and Xj be the values which appear on the three dice, respectively. Let Y be the maximum out of all three dice. (a) Find E(Y|X,-20 X2 = x) for x = 1, 2, . . . 6. (b) Find E(YX, -2). (2) Consider rolling three dice. Let X1, X2, and Xj be the values which appear on the three dice, respectively. Let Y be the maximum out of all three dice. (a)...
O. Let X1 and X2 be two random variables, and let Y = (X1 + X2)2. Suppose that E[Y ] = 25 and that the variance of X1 and X2 are 9 and 16, respectively. O. Let Xi and X2 be two random variables, and let Y = (X1 X2)2. Suppose that and that the variance of X1 and X2 are 9 and 16, respectively E[Y] = 25 (63) Suppose that both X\ and X2 have mean zero. Then the...
Questions 1-7: Hector will roll two fair, six-sided dice at the same time. Let A = the event that at least one die lands with the number 3 facing up. Let B = the event that the sum of the two dice is less than 5. 1. What is the correct set notation for the event that “at least one die lands with 3 facing up and the sum of the two dice is less than 5”? 2. Calculate the...