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 a random 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. a) Compute the expected value of Statistic M3, M4 and X by hand. b) Compute the variance of Statistic M3, M4 and X by hand. c) Compute the probability that Statistic M3, M4 and X is greater than or equal to $5, respectively.
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 a random 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.
a) Compute the
b) Compute the variance of Statistic M3, M4 and X by hand.
c) Compute the probability that Statistic M3, M4 and X is greater than or equal to $5,
respectively.
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