Let a random experiment be the cast of a pair of unbiased equal the smaller of the outcomes if they are different and the common value if they are equal. (a) With reasonable assumptions, find the p.m.f. of X. b) Draw a probability histogram. c) Let Y equal the range of the two outcomes, i.e., the absolute value of the let X

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2.1-8 Let a random experiment be the cast of a pair of unbiased six-sided dice and let X
equal the smaller of the outcomes if they are different and the common value if they
are equal.
(a) With reasonable assumptions, find the p.m.f. of X.
(b) Draw a probability histogram.
(c) Let Y equal the range of the two outcomes, i.e., the absolute value of the
difference of the largest and the smallest outcomes. Determine the p.m.f. g(y)
of Y for y = 0, 1,2,3, 4,5.
(d) Draw the probability histogram for g(y).
Transcribed Image Text:2.1-8 Let a random experiment be the cast of a pair of unbiased six-sided dice and let X equal the smaller of the outcomes if they are different and the common value if they are equal. (a) With reasonable assumptions, find the p.m.f. of X. (b) Draw a probability histogram. (c) Let Y equal the range of the two outcomes, i.e., the absolute value of the difference of the largest and the smallest outcomes. Determine the p.m.f. g(y) of Y for y = 0, 1,2,3, 4,5. (d) Draw the probability histogram for g(y).
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