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A box contains five slips of paper, marked $1, $1, $10, $25, and $25. The winner of a contest selects two slips of paper at random and then gets the larger of the dollar amounts on the two slips. Define a random variable w by w = amount awarded. Determine the probability distribution of w. (Hint: Think of the slips as numbered 1, 2, 3, 4, and 5, so that an outcome of the experiment consists of two of these numbers.)

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Answer:

w = $1 or $10 or $25

Probability distribution of w = ($1,$1  $1,$1  $1,$10  $1,$25  $1,$25  $1,$1  $1,$1  $1,$10  $1,$25  $1,$25  $10,$1  $10,$1  $10,$10  $10,$25  $10,$25  $25,$1  $25,$1  $25,$10  $25,$25  $25,$25  $25,$1  $25,$1  $25,$10  $25,$25  $25,$25)

Step-by-step explanation:

Since the winner gets the larger amount of the two slips picked, random variable 'w' which is the amount awarded could be $1 or $10 or $25.

The probability distribution of 'w' is the values that the statistic takes on. Which could be: $1,$1  $1,$1  $1,$10  $1,$25  $1,$25  $1,$1  $1,$1  $1,$10  $1,$25  $1,$25  $10,$1  $10,$1  $10,$10  $10,$25  $10,$25  $25,$1  $25,$1  $25,$10  $25,$25  $25,$25  $25,$1  $25,$1  $25,$10  $25,$25  $25,$25

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