XXX 1 X 2,..., X Let XX n f(x;0) = be a random sample from a distribution with density function Ox -¹, 0
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- A continuous random variable X has a uniform distribution on the interval [-3, 3]. Sketch the graph of its density function.5 Suppose the distribution function of the continuous random variable { is 1-es*, x20; F(x)=• 0, x3); (2) the density function f(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)
- A continous random variable has density function f(x)=(3x?)/(63) for Osxse, for some 0>0, and zero otherwise. What is the ratio of the mode to the median for this distribution? A. 2(1/3) B. 0/(21/3) O C.e D. 2(-1/3)Find the expected value of the continuous random variable g(x)= x^2+3x+2, if the density function for random variable x are shown in the following equation. f() = [F(2x-1) 0The total number of hours, in units of 100 hours, that a family runs a vacuum cleaner over a period of one year is a random variable X having the density function shown to the right. Find the variance of X (x-8). f(x)2-(X-8). 9sx< 10, 8Let X and Y be independent random variables. X is N(1,9) and Y is uniform on the interval {--1, 1]. Lat Write down the joint density for (X,Y) o Give the mean and variance of Y c) Give the median of X I dY Give the correlation coefficient p of X and YLet the random variable X have'the marginal density 1 f, (x)= 1, 1Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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