Question 1: Discrete Sampling Distribution A box contains ten sealed envelopes numbered 1, . . . , 10. The first three contain no money, the next five each contain $5, and there is a $10 bill in each of the last two. A sample of size N is selected with replacement (so we have arandom sample). Consider the following statistics:
Question 1: Discrete Sampling Distribution A box contains ten sealed envelopes numbered 1, . . . , 10. The first three contain no money, the next five each contain $5, and there is a $10 bill in each of the last two. A sample of size N is selected with replacement (so we have arandom sample). Consider the following statistics:
Statistic M3: The maximum amount in N = 3 randomly sampled envelopes
Statistic M4: The maximum amount in N = 4 randomly sampled envelopes
Statistic X: X = X1 + X2 - X3 where X equals the sum contained in the first two randomly
sampled envelopes minus the amount contained in the last randomly sampled envelope.
d) Compute the probability that Statistic M3, M4 and X is less than or equal to $2,
respectively.
g) Suppose you could pay $2 to keep the dollar amount obtained in either Statistic M3, M4 or
X. Which statistic offers the largest expected winnings? Which statistic has the highest
risk of your losing money (i.e. P(W < $0)? Note: If the statistic you choose has a negative
value, you would lose this amount in addition to the $2 wager.
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