Let a random experiment be the cast of a pair of unbiased dice, each having and let the random variable X denote the sum of the dice. (a) With reasonable assumptions, determine the p.m.f. f(x) of X. HINT: E outcome space consisting of the 36 points (result on first die, result die), and assume that each has probability 1/36. Find the probabilit possible value of X, namely, x = 2,3, 4,..., 12.

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2.1-7 Let a random experiment be the cast of a pair of unbiased dice, each having six faces.
and let the random variable X denote the sum of the dice.
(a) With reasonable assumptions, determine the p.m.f. f(x) of X. HINT: Picture the
outcome space consisting of the 36 points (result on first die, result on second
die), and assume that each has probability 1/36. Find the probability for each
possible value of X, namely, x = 2,3, 4,... , 12.
(b) Draw the probability histogram for f(x).
(c) Compute the mean u and the variance o² of the distribution.
Transcribed Image Text:2.1-7 Let a random experiment be the cast of a pair of unbiased dice, each having six faces. and let the random variable X denote the sum of the dice. (a) With reasonable assumptions, determine the p.m.f. f(x) of X. HINT: Picture the outcome space consisting of the 36 points (result on first die, result on second die), and assume that each has probability 1/36. Find the probability for each possible value of X, namely, x = 2,3, 4,... , 12. (b) Draw the probability histogram for f(x). (c) Compute the mean u and the variance o² of the distribution.
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Given information:

Given that two fair dice are rolled. The two random variables X1 = value on the first die and X2 = value on the second die.

Given random variable is X = sum{X1, X2}.

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