The manufacturer of a low-calorie dairy drink wishes to compare the taste appeal of a new formula (formula B) with that of the standard formula (formula A). Each of four judges is given three glasses in random order, two containing formula A and the other containing formula B. Each judge is asked to state which glass he or she most enjoyed. Suppose that the two formulas are equally attractive. Let Y be the number of judges stating a preference for the new formula. 2.1.1 The random variable Y follows a.............. .distribution. 2.1.2 Find the mean, variance and standard deviation of Y.

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The manufacturer of a low-calorie dairy drink wishes to compare the taste appeal of a new
formula (formula B) with that of the standard formula (formula A). Each of four judges is given
three glasses in random order, two containing formula A and the other containing formula B.
Each judge is asked to state which glass he or she most enjoyed. Suppose that the two formulas
are equally attractive. Let Y be the number of judges stating a preference for the new formula.
2.1.1
The random variable Y follows a
distribution.
2.1.2 Find the mean, variance and standard deviation of Y.
2.2
Use the uniqueness of moment-generating functions to give the distribution of a random
variable with moment-generating function m(t) = (0.8e + 0.2)7.
Transcribed Image Text:The manufacturer of a low-calorie dairy drink wishes to compare the taste appeal of a new formula (formula B) with that of the standard formula (formula A). Each of four judges is given three glasses in random order, two containing formula A and the other containing formula B. Each judge is asked to state which glass he or she most enjoyed. Suppose that the two formulas are equally attractive. Let Y be the number of judges stating a preference for the new formula. 2.1.1 The random variable Y follows a distribution. 2.1.2 Find the mean, variance and standard deviation of Y. 2.2 Use the uniqueness of moment-generating functions to give the distribution of a random variable with moment-generating function m(t) = (0.8e + 0.2)7.
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