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Question: In Problem of this section we allow two people of the same sex to sit side by side. If we require in addition to the condition that no husband and wife are side by side the condition that no two people of the same sex are side by side, we obtain a famous problem known as the m`enage problem. Solve this problem.
Problem: A group of n married couples sits a round a circular table for a group discussion of marital problems. The counselor assigns each person to a seat at random. What is the probability that no husband and wife are side by side?
Assuming that the population standard deviations are the same, perform a two independent samples t-test on the hypotheses Null Hypothesis: μ1 = μ2, Alternative Hypothesis: μ1 ≠ μ2. What is the test statistic and p-value of this test?
Let {Xn : n >=1} be a sequence of positive independent random variables with E(Xn) = c 2 (0; 1) for each n. Let Yn = X1X2...Xn, the product of the Xi's. Use Markov's inequality to prove that Yn ~ 0 in probability.
What is the difference between probability sampling and simple random sampling? Simple random sampling is a type of probability sampling.
In section you will learn about confidence intervals. Confidence intervals are often misinterpreted and commonly confused with the probability that something is likely to happen.
the manufacturer of an mp3 player wanted to know whether a 10 percent reduction in price is enough to increase the
the quarterly returns of a group of 59 mutual fund with the mean of 3.6 and standard deviation of 5.3 can be modeled by
Estimate the IQR of the tires tread life - If the dealer is only willing to give a refund to no more 2% of the customers, for what mileage can he guarantee these tires to last?
If a ball is selected at random from an urn containing three red balls, two white balls, and five blue balls.
Find out the following: Mean swipe rate, Standard deviation of the swipe rate.
(which cannot be proved in general without the axiom of choice, to be treated in §1.5). Hint: Let B be a countably infinite subset of X \Y . Then B and B ∪ Y have the same cardinality.
In the Distance problems, the kids are given a Rate (speed) that a vehicle is going, as well as a Time that the vehicle travels, and asked to calculate the Distance travelled. In the Rate problems they are asked to compute Rate from the other two ..
Find, as Cardano did, the expected total without finding its distribution - Large prizes were given for large totals with a modest fee to play the game. Explain why this could be done.
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