Question

In: Statistics and Probability

let x be the random variable in rolling two dice denotes the absolute difference between die...

let x be the random variable in rolling two dice denotes the absolute difference between die faces .

(i) find the probability distribution f(x) and cumulative distribution F(x) .

ii) plot f(x) and F(x)

iii) find the mean and variance of x and of g(x) = 3x + 7

Expert Solution

Outcome of rolling two dice is:

X : absolute difference between die faces

Probability density function
X	0	1	2	3	4	5
P(X=x)

cumulative distribution F(x)
X	0	1	2	3	4	5
F(X)

orchestra answered 2 years ago

Consider rolling two dice and let (X, Y) be the random variable pair defined such that...

Consider rolling two dice and let (X, Y) be the random variable pair defined such that X is the sum of the rolls and Y is the maximum of the rolls. Find the following: (1) E[X/Y] (2) P(X > Y ) (3) P(X = 7) (4) P(Y ≤ 4) (5) P(X = 7, Y = 4)

Let X be the random variable for the sum obtained by rolling two fair dice. (1)...

Let X be the random variable for the sum obtained by rolling two fair dice. (1) What is the probability density function? (2) What is the cumulative probability density function? (3) What is the expected value? (4) What is the variance?

Suppose we roll two fair dice. Let D1 be the random variable that denotes the value...

Suppose we roll two fair dice. Let D1 be the random variable that denotes the value of the first dice and D2 the sum of the numbers of both dice. a) Calculate the joint mass function of D1 and D2. b) Calculate the conditional mass function of D1 given D2 = d2. c) Calculate the conditional mass function of D2 given D1 = d1. d) Are the variables D1 and D2 independent? Argue your answer.

two fair dice are each rolled once. Let X denote the absolute value of the difference...

two fair dice are each rolled once. Let X denote the absolute value of the difference between the two numbers that appear. List all possible values of X Find the probability distribution of X. Find the probabilities P(2<X<5) and P(2£X<5). Find the expected value mand standard deviation of X.

Two fair dice are rolled and the outcomes are recorded. Let X denotes the larger of...

Two fair dice are rolled and the outcomes are recorded. Let X denotes the larger of the two numbers obtained and Y the smaller of the two numbers obtained. Determine probability mass functions for X and Y, and the cumulative distribution functions for X and for Y. Present the two cumulative distribution functions in a plot. Calculate E (2X + 2Y −8).

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 .

We roll two fair dice (a black die and a white die). Let x = the...

We roll two fair dice (a black die and a white die). Let x = the number on the black die − the number on the white die,record x as the outcome of this random experiment. (a) What is the probability space?

) Let X be the minimum of the two numbers obtained by rolling a die twice...

) Let X be the minimum of the two numbers obtained by rolling a die twice and Y the maximum. a) Compute E(X). b) Compute Var(X). c) Compute E(Y).

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...

1. Suppose that you roll two dice simultaneously. Let X be the random variable that gives...

1. Suppose that you roll two dice simultaneously. Let X be the random variable that gives the product of the two die outcomes. Let f(x) = P(X = x) be the probability distribution for X. (a) Is X discrete or continuous? (b) What is f(12)? (c) If F(x) is the cumulative distribution function, what is F(4)?