Two fair dice are thrown. Let X be the number of 5’s and Y be the...

Two fair dice are thrown. Let X be the number of 5’s and Y be the number of 6’s.

Find (a) the joint PMF of X and Y,

(b) the two marginal distributions (PMFs),

and (c) the conditional distribution (PMF) of Y given X = x for each possible value of X.

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

You roll two fair dice, and denote the number they show by X and Y. Let...

You roll two fair dice, and denote the number they show by X and Y. Let U = min{X, Y } and V = max{X, Y }. Write down the joint probability mass function of (U, V ) and compute ρ(U, V ) i.e the correlation coefficient of U and V

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).

Two fair dice are tossed together. Let X be the sum and Y the product of...

Two fair dice are tossed together. Let X be the sum and Y the product of the two numbers on the top of the dice. Calculate E(X+ 3Y).

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 fair dice are tossed, and (X,Y) denote the number of spots on the first and...

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 <= U <= 7 | W <= 1]

Three fair dice are rolled. Let S be the total number of spots showing, that is...

Three fair dice are rolled. Let S be the total number of spots showing, that is the sum of the results of the three rolls. a) Find the probabilities P(S = 3), P(S = 4), P(S = 17), P(S = 18). b) Find the probability P(S ≥ 11).

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.

Roll 3 times independently a fair dice. Let X = The # of 6's obtained. The...

Roll 3 times independently a fair dice. Let X = The # of 6's obtained. The possible values of the discrete random variable X are: 1.For the above random variable X we have P(X=2) equal to: 2.For the above random variable X we have P(X=3) equals to: 3.For the above random variable X we have P(X=3) equals to: 4.The Domain of the moment generating function of the above random variable X is: 5.The Domain of the moment generating function of...

Let a random experiment consist of tossing two fair six sided dice. Let x be the...

Let a random experiment consist of tossing two fair six sided dice. Let x be the minimum number shown on the dice. Determine the closed form PMF of x. Hint: Creating a chart for all possible combinations of the two rolls may be helpful.

Suppose two fair dice are rolled. Let X denote the product of the values on the...

Suppose two fair dice are rolled. Let X denote the product of the values on the dice and Y denote minimum of the two dice. Find E[X] and E[Y] Find Var X and Var Y Let Z=XY. Find E[Z]. Find Cov(X,Y) and Corr(X,Y) Find E[X|Y=1] and E[Y|X=1]

Subjects