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Let S be a random variable (not necessarily positive). Prove using Markov's inequality that for every p>0 and for every constant q,
P(S>=a) (=<) exp(-pq)E(exp(pS))
Here >= denoted greater than or equal to, and =< denotes less than or equal to.
Test hypothesis that average price of gasoline in western states is higher than national average for Continental USA and the District of Columbia, i.e., higher than $3.74.
Any value which is based on having measured a sample is called:
Develop a regression model that could be used to predict the final average in the course based on the first test grade. Predict the final average of a student who made an 83 on the first grade.
What is coefficient of determination? Calculate F statistic. (Hint: You must complete the table to answer the question.)
Looking at the data, you suspect that the manufacturer is incorrect in its label claim. You want to perform hypothesis testing to prove or disprove it.
Can you determine the number of levels used for each factor? Explain. Describe a treatment for this experiment and determine the number of treatments used.
Constructing a 95% confidence interval for the true length of time for all pepper seeds to germinate you must calculate the margin of error. The margin of error in this case is 0.60.
In studying the performance of the comapany's stock investments over the past year, the research manager of a mutual fund company finds that only 43% of the stocks returned more than the rate that had been expected at the beginning of the year.
Suppose that 98% of the customers in your market have Internet access, and you select a random sample of 500 customers. What is the probability that the sample has:
The mean SAT verbal score is 478, with a standard deviation of 98. Use the Empirical Rule to determine what percent of the scores lie between 380 and 478. (Assume the data set has a bell-shaped distribution)
You're a risk manager of ABC company and you are reevaulating your insurance contract. Your insurer has informed you that the expected value of frequency per month for ABC is 2.43.
Construct the 95% confidence interval estimate of the mean number of migraine attacks for those treated with acupuncture.
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