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Exam 1 Solution

# So in the present problem you would reason the first

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Unformatted text preview: sequence of integers {1,...,12} whose last element is 7 (for July) and whose other elements are all different from 7. The sample space is then the infinite set of all such sequences, and the probability of any sequence of length n is 12- n. Alternatively, you can define the outcome as the length of such a sequence- - - that is, the number of people you had to sample. In this case the sample space is the set of all positive integers and the probability assigned to n Reason. When we sample with replacement, the !! !!! ! is !" . This is identical to the PMF of the random variable in part (b). !" (b) Now consider the random variable X whose value is the number of people sampled until the July birthday appeared. Sketch the PMF for this random variable as a stem plot. I'm not so interested in the exact values as in the general shape and extent of the graph. Solution. The PMF is shown in the figure: it is infinite in extent...
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