Two fair dices, X and Y , are tossed separately. Let A, B and C represent...

Two fair dices, X and Y , are tossed separately. Let A, B and C represent the following three events. A: You got an odd number from die X. B: You got an even number from die Y . C: The sum of two dice is an odd number. Whether A, B, C are independent? Explain!

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orchestra answered 2 years ago

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

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4 fair coins are tossed. Let X be the number of heads and Y be the...

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Two fair dice are tossed. Let A be the maximum of the two numbers and let...

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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]

A fair coin is tossed r times. Let Y be the number of heads in these...

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Two rolls of a fair die. Let x and y be the results of the two...

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Suppose two fair sided die with sides labeled 1,2,3,4,5,6 are tossed independently. Let X = the...

Suppose two fair sided die with sides labeled 1,2,3,4,5,6 are tossed independently. Let X = the minimum of the value from each die. a. What is the probability mass function(pmf) of X? b. Find the mean E[X] and variance V (X). c. Write the cumulative distribution function (cdf) of X in a tabular form. d. Write F(x) the cdf of X as a step function and give a rough sketch for this function.

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

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A fair coin is tossed two times, and the events A and B are defined as...

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A fair coin is tossed four times. Let X denote the number of heads occurring and...

A fair coin is tossed four times. Let X denote the number of heads occurring and let Y denote the longest string of heads occurring. (i) determine the joint distribution of X and Y (ii) Find Cov(X,Y) and ρ(X,Y).

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