2 dice are rolled. Let X be the number on the first die, Y - on...

2 dice are rolled. Let X be the number on the first die, Y - on the second, and Z=X - Y. Find the expectation and standard deviation of Z.

Expert Solution

X\Y	1	2	3	4	5	6
1	0	-1	-2	-3	-4	-5
2	1	0	-1	-2	-3	-4
3	2	1	0	-1	-2	-3
4	3	2	1	0	-1	-2
5	4	3	2	1	0	-1
6	5	4	3	2	1	0

V(X)=5.83-0^2=5.83

So standard deviation is

orchestra answered 2 years ago

a die is rolled 6 times let X denote the number of 2's that appear on...

a die is rolled 6 times let X denote the number of 2's that appear on the die. 1. show that X is binomial. 2. what is the porbaility of getting at least one 2. 3. find the mean and the standard deviaion of X

2. Three fair dice are rolled. Let X be the sum of the 3 dice. (a)...

2. Three fair dice are rolled. Let X be the sum of the 3 dice. (a) What is the range of values that X can have? (b) Find the probabilities of the values occuring in part (a); that is, P(X = k) for each k in part (a). (Make a table.) 3. Let X denote the difference between the number of heads and the number of tails obtained when a coin is tossed n times. (a) What are the possible...

Two fair dice are rolled. Let X be the product of the number of dots that...

Two fair dice are rolled. Let X be the product of the number of dots that show up. (a) Compute P(X = n) for all possible values of n. (b) Compute E(X). (c) Compute Var(X) and SD(X).

A pair of dice are rolled. Let A be the event as “the first dice roll...

A pair of dice are rolled. Let A be the event as “the first dice roll is 3” and event B as “the second dice roll is 4”. Let event C be as “the sum of the dice rolls are 7.” a) Show that A and B are independent, that A and C are independent, and that B and C are independent. b) Show that A, B, and C are not mutually independent.

A fair die is rolled twice. Let X and Y be the smallest and largest, respectively,...

A fair die is rolled twice. Let X and Y be the smallest and largest, respectively, number that appears in the two rolls. (a) Determine the probability mass function of (X, Y). (Write a formula forP(X=i, Y=j)or give a table of values.) (b) Are X and Y independent? (c) Find E(X+Y). (Give your answer as a decimal number.)

Two dice are rolled. Let X be the random variable representing the result of the first...

Two dice are rolled. Let X be the random variable representing the result of the first die, and Y be the random variable representing the largest value rolled on either die. Describe the joint probability density function for X and Y .

Two fair dice are rolled at once. Let x denote the difference in the number of...

Two fair dice are rolled at once. Let x denote the difference in the number of dots that appear on the top faces of the two dice. For example, if a 1 and a 5 are rolled, the difference is 5−1=4, so x=4. If two sixes are rolled, 6−6=0, so x=0. Construct the probability distribution for x. Arrange x in increasing order and write the probabilities P(x) as simplified fractions.

Two dice are rolled. Let the random variable X denote the number that falls uppermost on...

Two dice are rolled. Let the random variable X denote the number that falls uppermost on the first die and let Y denote the number that falls uppermost on the second die. (a) Find the probability distributions of X and Y. x 1 2 3 4 5 6 P(X = x) y 1 2 3 4 5 6 P(Y = y) (b) Find the probability distribution of X + Y. x + y 2 3 4 5 6 7 P(X...

Dice Suppose that a red die and a green die are rolled and the numbers on...

Dice Suppose that a red die and a green die are rolled and the numbers on the sides that face upward are observed. (See Example 7 of this section and Example 2 of the first section.) (a) What is the probability that the numbers add up to 9? (b) What is the probability that the sum of the numbers is less than S?

A die is rolled and, independently, a coin is tossed. Let X be the value of...

A die is rolled and, independently, a coin is tossed. Let X be the value of the die if the coin is H and minus the value of the die if the coin is T. (a) Calculate and plot the PMF of X. (b) Calculate E [X] and var(X) (c) Calculate and plot the PMF of X 2 − 2X. 2. A drunk walks down a street. Assume he starts at block 0. Every 10 minutes, he moves north a...

Question