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For i.i.d. variables X1, X2,... , let An be the smallest σ -algebra for which X1,..., Xn are measurable and Bn the smallest σ -algebra for which Xn+1, Xn+2,... , are measurable. Let Sn be the σ -algebra of sets in An whose indicator functions are symmetric functions of X1,..., Xn . Let Cn be the σ -algebra generated by Sn and Bn . Show that for any sequence of U -statistics {Un, n ≥ m} generated as above by a random variable f (X1,..., Xm ) with f symmetric and EQ | f | ∞, {Un, Cn }n≥m is a reversed martingale.
Calculate the MEAN and STANDARD DEVIATION for the distribution below:
Solve the differential equation, 12y=by-4y' writing the solution as y as a function of x (isolating y).
What's the probability that among three randomly selected high school students
Distributed with mean 4.6 minutes and standard deviation 1.4 minutes. If there are 75 students in class, determine probability the professor requires more than 6 hours to mark all of the midterms?
One of the criteria in their evaluation was the baggage capacity of the boat, evaluated using a 4-point rating scale from 1 to 4.
question given here are the data from a dependent variable and two independent variables. the second independent
water vapor initially at 3.0 mpa and 300oc state 1 is contained within a piston-cylinder assembly. the water is cooled
A simple random sample of 60 voters will be drawn from this population. The chance the sample contains only Republicans and Democrats is?
1. Let (X, S, µ) be a finite measure space, meaning that µ(X ) ∞. A se- quence { fn } of real-valued measurable functions on X is said to converge in measure to f if for every ε> 0, limn→∞ µ{x : | fn (x ) - f (x )| > ε}= 0. Show that if fn → f in ..
In the following regression, X = total assets ($ billions), Y = total revenue ($ billions), and n = 64 large banks. (a) Write the fitted regression equation.
mary took a test and her score was the 85th percentile.which of the following is a true statement about marys score?a.
Test the whether the attitude toward keeping weight down associated with smoking status.
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