A pair of fair dice is tossed. Let X denote the larger of the two numbers showing. Find the expected value of X.
A pair of fair dice is tossed. Let X denote the larger of the two numbers...
Two fair dice are tossed independently, and the pair, (X, Y), denote the number of spots on the first and on the second dice. Consider two random variables: U = X + Y and W = X-Y! 1. Find the distribution of U. 2. Find the distribution of W. 3. Find the conditional distribution of W, given that U 6
Two fair 6-sided dice are tossed. Let X denote the number appearing on the first die and let y denote the number appearing on the second die. Show that X, Y are independent by showing that P(X = x, Y = y) = P(X = x) x P(Y = y) for all (x,y) pairs.
Roll two fair six-sided dice, and let X, Y denote the first and the second numbers.If Z=max {X, Y}, find- E(Z)- V(Z)If Z=|X-Y|, find- E(Z)- V(Z)
(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).
Question 5: Roll two fair dice and let X be the sum of the two numbers faced up. a. Find the probability distribution of X . b. What is the expected value of X? c. What is the variance of X ?
2.6 Suppose two dice are tossed and the numbers on the upper faces are observed. Let S denote the set of all possible pairs that can be observed. [These pairs can be listed, for example, by letting (2, 3) denote that a 2 was observed on the first die and a 3 on the second.] a Define the following subsets of S: A: The number on the second die is even. B: The sum of the two numbers is even....
Problem 5 Two fair dice are tossed, and ((X,Y) denote the number of spots on the first and on the second dice. Consider two random variables: U = X + Y and W - X - Y . (A) Derive the distribution of U. List all possible values and evaluate their probabilities. (B) Derive the distribution of W. List all possible values and evaluate their probabilities. (C) Determine the conditional probability P (6 SU <71W <1]
3. Two fair dice are thrown. Let X be the smaller of the two numbers obtained (or the common value if the same number is obtained on botih dice). Find the probability mass function of X. Find P(X>3).
A pair of fair dice is tossed. Events A and B are defined as follows. A: The sum of the numbers on the dice is 5 B: At least one of the numbers 2 (a) Identify the sample points in the event P(A B). (b) Identify the sample points in the event P(A B). (c) Find P(A B). (d) Find P(A B). (e) Are A and B independent events? We were unable to transcribe this imageWe were unable to transcribe...
In a board game a pair of dice are tossed at the same time. The higher the sum of the two numbers, the better. Calculate the expected value of the sum of the two numbers.