Suppose you roll two ordinary dice. Calculate the expected value of their product. Solve using R...

Suppose you roll two ordinary dice. Calculate the expected value of their product. Solve using R studio coding.

Expert Solution

orchestra answered 1 year ago

suppose you roll two fair dice. A) what is the probability that you will roll an...

suppose you roll two fair dice. A) what is the probability that you will roll an even number on the first die AND a 5 on the second die B) What is the probability that the sum of the numbers on the two dice is 9? show all work.

Suppose we would roll two standard 6-sided dice. (a) Compute the expected value of the sum...

Suppose we would roll two standard 6-sided dice. (a) Compute the expected value of the sum of the rolls. (b) Compute the variance of the sum of the rolls. (c) If X represents the maximum value that appears in the two rolls, what is the expected value of X? What’s the probability of sum = 7?

Roll two ordinary dice and let X be their sum. Draw the pmf and cmf for...

Roll two ordinary dice and let X be their sum. Draw the pmf and cmf for X. Compute the mean and standard deviation of X. Solve using R studio coding.

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.

You roll two fair dice. Let A be the event that the sum of the dice...

You roll two fair dice. Let A be the event that the sum of the dice is an even number. Let B be the event that the two results are different. (a) Given B has occurred, what is the probability A has also occurred? (b) Given A has occurred, what is the probability B has also occurred? (c) What is the probability of getting a sum of 9? (d) Given that the sum of the pair of dice is 9...

Suppose you roll two 6 sided dice, letting X be the sum of the numbers shown...

Suppose you roll two 6 sided dice, letting X be the sum of the numbers shown on the dice and Y be the number of dice that show an odd number. a) Find the joint pmf of <X,Y> b) Find the marginals pmf's for both variables. c) Are X and Y independent?

Suppose you roll two 6 sided dice, letting X be the sum of the numbers shown...

Suppose you roll two 6 sided dice, letting X be the sum of the numbers shown on the dice and Y be the number of dice that show an odd number. a) Find the joint pmf of <X,Y> b) Find the marginals pmf's for both variables. c) Are X and Y independent?

Suppose you roll two 6-sided dice, letting X be the sum of the numbers shown on...

Suppose you roll two 6-sided dice, letting X be the sum of the numbers shown on the dice and Y be the number of dice that show an odd number. a) Find the joint pmf of <X,Y> b) Find the maringals pmf's for both variables. c) Are X and Y independent?

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)?

This problem concerns the dice game craps. On the first roll of two dice, you win...

This problem concerns the dice game craps. On the first roll of two dice, you win instantly with a sum of 7 or 11 and lose instantly with a roll of 2,3, or 12. If you roll another sum, say 5, then you continue to roll until you either roll a 5 again (win) or roll a 7 (lose). How do you solve for the probability of winning?

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Suppose you roll two ordinary dice. Calculate the expected value of their product. Solve using R...

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