Let f, g be probability densities such supp(f) c supp(g). show yes iid. L(g) X1,..., Xn then f(X;) Wi g(X;) is hopeful 1. Argue why the weights need to be re-normalized even when the normalization constants of the densities f and g are known.
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- Example 3: The probability density ƒ(x) of a continuous random variable is given by f(x) 3 ce , -mIf the prob density of a rv is given by f(x)=kx² 04. The monthly revenue (in millions) of a local gaming company is represented by a continuous random variable X having the probability density f(x) = (1 - (x-1)²), 0 < x < 2, 0, elsewhere Find the mean and variance of X.Q5/ Let X1, ., X,n be a r.s. from population with p. d.f. f(x) = 0, 0> x>0* 0.W. X(1) Let X(1) < .. < X(n) be the order statistics. Find the p. d. f. of U = ) %3D X(n)Prof that' For a fixed B with P(B) > 0, P(A l B) is probability function.5. Let 0 and a be parameters. Show that the family of functions fo,a(x) = I > 0 (x+0)a+1³ is a probability density function. What can you say about the mean of a random variable that has fo,a as a pdf?* Consider the probability density function fx (x) = a e-b lel where X is the random %3D variable which assumes all the values from (i) relation between a and b -00 to -00, Find (ii) the probability of finding X in the range 1 to 2.الموافق foo an exponentiaL distribution fx Cx jt) e.w. where u>o Write (Dankderive) meancespedoed V9lue) f.eECx)Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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