Experiment consists of tossing a fair coin
Suppose an experiment consists of tossing a fair coin until a three heads occur. What is the probability that the experiment ends after exactly six flips of the coin with a head on the fifth toss as well as on the sixth?
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Suppose that Y is a binomial random variable based on n trials and success probability p. Use the conjugate beta prior with parameters a and b to derive the posterior distribution of p|y.
A test consists of 10 true/false questions. To pass the test a student must answer at least 7 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?
Suppose that an ink cartridge is classified as being overfilled, medium filled, or underfilled with a probability of 0.40, 0.45, and 0.15, respectively. What is the probability that a cartridge is classified as not underfilled?
Calculate the probability of observing a sample proportion of voters 0.55 or higher supporting the incumbent governor
A die is rolled and the square of the number of dots is recorded as the random variable X (for example, a roll of 3 results in X=9). Find the expected value and standard deviation of the random variable x.
Distribution of systolic and diastolic blood pressure for female diabetes between the ages of 30 and 34 have unknown means. The standard deviation are s=11.8mm Hg and d= 9.1mm Hg respectively [8].
All the major stock market indexes posted heavy losses in 2008. The mean one-year return for stocks in the S&P 500, a group of very large companies, was -38.5%.
What happens to the standard deviation of the distribution of sample means (DSM) as the sample size increases? Does the standard deviation of the DSM also increase? Why or why not? Explain.
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