1. Suppose we have two jars. The first jar contains 4 white and 6 black marbles while the second
one contains 4 white and 3 black marbles. One marble is drawn at random from one of the jars,
and it is found to be black. Find the probability that it was drawn from the first jar.
Hint: Probability of selecting jar 1 and jar 2 is the same.
To answer problems 2 through 5, consider the random experiment of rolling two fair, distinct dice. Let ??
be the maximum of the two numbers. Recall, for example, max (12, 15) = 15 and max (10, 10) = 10.
2. Determine the probability mass function ??(??).
3. Determine the cumulative distribution function ??(??).
4. Find the expected value ??(??) = ??.
5. Find the variance ??(??) = ?? 2 .
R Part
Let
??
1
3
7
11 15 21
23
37
??(??) 0.1 0.2 0.2 0.1 0.1 0.05 0.05 0.2
1. Find the expected value ??(??) = ??.
2. Find the variance ??(??) = ?? 2 .
3. Determine the cumulative distribution function ??(??) (by hand).
4. Graph the probability mass function.
5. Graph the cumulative distribution function.

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