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You get to choose between two envelopes, each of which contains a check for some positive amount of money. Unlike in the two-envelope paradox, it is not given that one envelope contains twice as much money as the other envelope. Instead, assume that the two values were generated independently from some distribution on the positive real numbers, with no information given about what that distribution is. After picking an envelope, you can open it and see how much money is inside (call this value x), and then you have the option of switching. As no information has been given about the distribution, it may seem impossible to have better than a 50% chance of picking the better envelope. Intuitively, we may want to switch if x is "small" and not switch if x is "large", but how do we define "small" and "large" in the grand scheme of all possible distributions? [The last sentence was a rhetorical question.] Consider the following strategy for deciding when to switch: create a threshold T ~Expo(? = 1), and switch envelopes if and only if the observed value x is less than the value of T. Show that this strategy succeeds in picking the envelope with more money with probability strictly greater than 1/2. Hint: Let t be the value of T (generated by a random draw from the Expo(1) distribution). First explain why the strategy works very well if t happens to be in between the two envelope values, and does no harm in any other case (i.e., there is no case in which the strategy succeeds with probability strictly less than 1/2).
construct a 95 confidence interval to estimate the population proportion with a sample proportion equal to 0.60 and a
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Write a short paragraph that highlights your understanding of why exploratory data analysis is a critical part of any analytical strategy- create a scatterplot that includes a regression line. The variables you will use are: Exam Performance and Ex..
What is the probability that a respondent said neither the Big Ten nor the Pac-10 will have a team in the Rose Bowl?
What type of probability distribution is appropriate for this problem? Determine the probability of getting no calls between eight and nine in the morning. Calculate the probability of getting exactly five calls between eight and nine in the morning
an anova procedure is used for data obtained from five populations. five samples each comprised of 20 observations were
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A True-False test was developed for a Risk Management class. A student, who didn't study, decided to randomly guess the answer on each question.
With a mean of $70,000 and a standard deviation of $20,000. A loan application is received this morning. What is the probability: a. The amount requested is $80,000 or more?
If 1.5 million X-Games were sold over the holidays, determine an interval for the number of defectives in sales. 12,184 to 32,816.
A coin is unbalanced such that it comes up tails 55% of the time. In an effort to prove that the coin is unfair, an experimenter flips the coin 50 times.
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