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As in Problem 4 in §10.1, let X1, X2,... , be i.i.d. real random variables with E |X1| ∞. Let Sn := X1 +· · · + Xn . For n = 1, 2,... , let T-n := Sn/n. Let B-n be the smallest σ-algebra for which Sk are measurable for all k ≥ n. Show that {Tk, Bk }k≤-1 is a reversed martingale and {|Tk |, Bk }k≤-1 is a reversed submartingale.
an oil exploration company currently has two active projects one in asia and the other in europe. let a be the event
Find the equation of the regression line to predict course grades from placement test scores.
A survey of Ohio University students was conducted to determine if there was a particular Green that was desired by students to live on. A sample of students responses are reproduced below. Do students prefer a particular Green? Use critical value..
25% of the residents garden. If 5% of the residents play poker and garden, find the probability that a resident plays poker, given that they also garden.
State the null and alternative hypotheses using proper Statistical Notation
a missile guidance system has five fail-safe components. the probability of each failing is 0.05. find these
according to a survey of 25000 households conducted by nielson company 51 of the people watching the 2010 super bowl
A random variable has a normal distribution with ?? = 62.4. Find the standard deviation of the random variable if the probability is 0.20 that it will take on a value greater than 79.2
when an events probability depends on the likelihood of another event the probability is aa conditional probability.b
if two random samples of size 400 are drawn from two populations that have standard deviations of 60 and 8 respectively
Based on a survey of over 10,000 households, the number of televisions in the home was recorded as given in the table below. Based on the data, find the expected number of televisions in a home.
Martin Motors has in stock three cars of the same make and model. The president would like to compare the gas consumption of the three cars (labeled car A, car B, and car C) using four different types of gasoline. For each trial, a gallon of gasoline..
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