(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) Fi...
(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...
(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)...
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.
3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1 < x2 < X3. Suppose that y = ax + by + c is a parabola passing through the three points (x1, yı), (x2, y), and (x3, Y3). We have that a, b, and c must satisfy i = ax + bx + C V2 = ax + bx2 + c y3 = ax} + bx3 + c Let D = x X2 1....
Let Xi Pn(2) and X2 Pn(5) be two independent random variables and it that y = Xi + X-Pn(7). is shown (a) Given Y-n, n 20, what are the possible values of X1? (b) Calculate the conditional distribution of Xi given Y-n for n 2 0. Let Xi Pn(2) and X2 Pn(5) be two independent random variables and it that y = Xi + X-Pn(7). is shown (a) Given Y-n, n 20, what are the possible values of X1? (b)...
Let X1, X2, and X3 represent the times necessary to perform three successive repair tasks at a certain service facility. Suppose they are independent, normal rv's with expected values μ1, μ2, and μ3 and variances σ12, σ22, and σ32, respectively. (Round your answers to four decimal places.) LetX1 X2 and X3 represent the times necessary to perform three success ve epa r tasks at a certain service facility. Suppose they are independent normal rv's with expected values μι μ2 and...
Conditional expectations Let 2 - 0, 1)3, that is, all possible (ordered) triples of zeros and ones. Suppose that all outcomes have equal probability. We define three random variables Xi, X2, and X3 on this space representing the first, second, and third digit, respectively. We also define (i) Compute the values (across S2) of each of the following random variables: (i) What is the probability mass function of E(X2 X)
Consider three six-sided dice, and let random variable Y = the value of the face for each. The probability mass of function of Y is given by the following table: y 1 2 3 4 5 6 otherwise P(Y=y) 0.35 0.30 0.25 0.05 0.03 0.02 0 Roll the three dice and let random variable X = sum of the three faces. Repeat this experiment 50000 times. Find the simulated probability mass function (pmf) of random variable X. Find the simulated...
Problem 4 [10 points Assume that variables, (X1, X2, with the same Consider Y-Σ, xi. АЗ, }, conditionally, given Q, are independent Bernoulli distributed parameter, Q. The marginal distribution of Q is uniform over the unit interval (o, Hint Use the identity (valid for integer a 20 and b 2 0): a! b! 1. Find marginal distribution of Y, for k 0,1,2,3. 2. Derive the conditional density for Q, given that Y -2 3. Derive conditional expectation and conditional variance...
Let the mutually independent random variables X1, X2, and X3 be N(0, 1),N(2, 4), and N(−1, 1), respectively. Compute the probability that exactly two ofthese three variables are less than zero.