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Two fair six-sided dice are tossed independently. Let M = the maximum of the two tosses (so M(1,5) = 5, M(3,3) = 3, etc.). (a) What is the pmf of M? [Hint: First determine p(1), then p(2), and so on.] (Enter your answers as fractions.)

User Gkucmierz
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Final answer:

The probability mass function (pmf) of M, the maximum of two tosses with fair six-sided dice, can be determined by finding the probability of each value of M.

Step-by-step explanation:

The probability mass function (pmf) of M, the maximum of two tosses with fair six-sided dice, can be determined by finding the probability of each value of M.

To find p(1), we need to consider the possible outcomes when the maximum value is 1. Since both dice need to show a value less than or equal to 1, there is only one possible outcome, (1,1). Therefore, p(1) = 1/36.

We can follow a similar approach to find the probabilities for the other values of M. For example, p(2) is the probability that the maximum value is 2. The possible outcomes are (1,2), (2,1), and (2,2). So, p(2) = 3/36 = 1/12.

Using this method, we can determine the probabilities for the remaining values of M: p(3) = 5/36, p(4) = 7/36, p(5) = 9/36 = 1/4, and p(6) = 11/36. Therefore, the pmf of M is:

p(1) = 1/36

p(2) = 1/12

p(3) = 5/36

p(4) = 7/36

p(5) = 1/4

p(6) = 11/36

User Akshaypjoshi
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