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.

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Suppose we roll a fair dice thrice in such a way that the assumption of random...

Suppose we roll a fair dice thrice in such a way that the assumption of random sampling is satisfied. Let {X1;X2;X3} be the numbers coming up in the first three throws. Let their sample average be X3= (1/3) * ((X1+X2+X3)) 1) Write down the sampling distribution ofX3. To this end, you need to write down a table that contains all values that X3 can take on together with their probabilities. 2) What is the probability that X3 greater than equal...

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)?

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...

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

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).

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.

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?

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

Roll two fair dice. Each die has six faces. A. Let A be the event that...

Roll two fair dice. Each die has six faces. A. Let A be the event that either a 3 or 4 is rolled first followed by an odd number. P(A) = Round your answer to two decimal places. B. Let B be the event that the sum of the two dice is at most 7. P(B) = Round your answer to two decimal places. C. Are A and B mutually exclusive events? (Yes or No) D. Are A and B independent or...

Fair Dice We roll a fair dice 10 times and register how many times we obtained...

Fair Dice We roll a fair dice 10 times and register how many times we obtained 5. (a) Find the probability to obtain 5 seven times. (b) Estimate the number of fives that will come out with the probability 0.35. (c) What is the probability of geting 30 fives when rolling a fair dice 45 times? (d) How many fives will come out with a probability of 0.25, when rollong a fair dice 45 times?

Subjects