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Under H0 , a random variable has the cumulative distribution function F0 (x) = x2 , 0 ≤ x ≤ 1; and under H1 it has the cumulative distribution function F1(x) = x3, 0 ≤ x ≤ 1.
(a) If the two hypotheses have equal prior probability, for what values of x is the posterior probability of H0 greater than that of H1?(b) What is the form of the likelihood ratio test of H0 versus H1?(c) What is the rejection region of a level α test?(d) What is the power of the test?
Find the mass and center of masss of the solid S bounded by the paraboloid z= 4x^2 + 4y^2 and the plane z= a (a is greater than 0) if S has constant density K.
Analyzing the use of large samples in surveys - Give your understanding of why people doing polling and opinion surveys
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We are learning Rolle, Lagrange, Fermat, Taylor Theorems in our Real Analysis class. We just finished continuity and are now studying differentiation.
Student arrive at the Administrative Services Office at an average of one every 15 minutes, and their requests take on average 10 minutes to be processed.
Find the variation constant and an equation of variation where y varies directly as x and y= 72 and x=8
Find the mean and variance of theses draws
A number (a) is called a fixed point of a function (f) if f(a)=a. Prove that, if f'(x) does NOT equal 1 for all real numbers (x), then f has at most one fixed point.
A ship embarked on a long voyage. At the start of the voyage, there were 500 ants in the cargo hold of the ship. One week into the voyage, there were 800 ants. Suppose the population of ants is an exponential function of time.
Probability : Dice and Payoff c) in part a, if you bet one dollar that a sum of 10 will turn up, what should the house pay (plus returning your one dollar bet) if a sum of 10 turns up for the game to be fair?
Find (and describe) all the regular tessellations of the plane. Note that septagons, nonagons, and 11-gons are not provided. How do you know each one you find really fills in all the gaps around a vertex point? How do you know when you're done?
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