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1. An urn contains n white and m black balls that are removed one at a time. If n > m, show that the probability that there are always more white than black balls in the urn (until, of course, the urn is empty) equals (n - m)/(n + m). Explain why this probability is equal to the probability that the set of withdrawn balls always contains more white than black balls. (This latter probability is (n - m)/(n + m) by the ballot problem.)
2. A coin that comes up heads with probability p is ?ipped n consecutive times. What is the probability that starting with the ?rst ?ip there are always more heads than tails that have appeared?
Among 12 adults randomly selected from this area, only 3 reported that their health was excellent. Find the probability that when 12 adults are randomly selected, 3 or fewer are in excellent health.
Thirty accidents of these vans were examined, and 11 vans had rolled over. Test the claim that the proportion of rollovers exceeds.
The sample standard deviation is $2,050. Using this information, calculate the 95% confidence interval (rounded to the nearest $10). Interpret your findings.
Find the probability that not enough seats will be available. Is this probability low enough so that overbooking is not a real concern?
the heights of people of the same sex and similar ages follow a normal distribution reasonably closely. weights on the
By taking the Laplace transform and using the convolution theorem, obtain the solution of the integral equation f(t) = 1+t+int[(t-u)f(u)du,u=0..t)
A person claims to be able to predict the outcome of flipping a coin. This person is correct 16/25 times. Compute the 95% confidence interval on the proportion of times this person can predict coin flips correctly.
The question is, is it just sampling error that accounts for the difference, or is the local store different than the national numbers? This is a typical chi-square problem.
q1. explain the difference between multiple independent variables and multiple levels of independent variables. which
Develop a model for determining how many people should be sent to contain the fire and for determining the best location for the firebreak.
What are the main drivers of uk banks' profitability? what are the implications of increased concentration in the uk banking market? what were the main recommendations of the cruickshank report and how did the industry respond?
question how are the degrees of freedom for the chi-square hypothesis tests different from those of most other
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