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(a) Construct a martingale that converges to -∞ a.s. as n → ∞.
Sums of independent random variables with mean 0 are usually a good try.
(b) Construct a non-negative sub martingale that converges to 0 a.s. as n → ∞.
Since the stock market began in 1872, there have been two consecutive losing years eight times. In six of those cases, the market rose during the following year
A random sample of 100 adult workers, 60 men and 40 women, is selected in a large Midwestern city. Of the group, 42 men and 17 women are union members.
Sketch an indifference curve that reflects the way you would trade off rent versus proximity to campus. Is your indifference curve a straight line?
A ball is drawn from a bag containing 13 red balls numbered 1-13 and 5 white balls numbered 14-18.
We related EVPI to the value of an envelope that contains the true ultimate outcome. This concept can be extended to "less than perfect" information.
Estimate the average number of minutes longer a woman must work out at light exertion than at heavy exertion to get the same benefit
The following data are daily price quotations of two stocks:
Conduct a hypothesis test to determine whether there is any evidence that the true mean value of Y for x = 11.5 is different from 5.
suppose we have a floor made of parallel strips of wood each with width 3 and we drop a needle of length 1 onto the
(a) Obtain the moment-generating function of the random variable N{t + S). Indication. If X has a Poisson distribution with parameter a, then Mx(t) = exp{α(et - 1)}.
Find a 98% confidence interval for the mean number of days required for successful completion of physical therapy for patients in the average group. Discuss the results.
1. Calculate the residuals from the least-squares fitted model for the pH mea surement data set phmeas .txt and plot them against the fitted values. What does this indicate about the fitted model?
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