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- TThe joint probability density function of random variables X and Y is [xy 0sx<1, 01. Let X1,..., X, be a random sample from a distribution with pdf f(x) = 2x, 0< x < 1. Compute the joint density of the smallest and the largest order statisics.7. Let X and Y be continuous random variables with joint probability density function given by fxy(xy): Sc, (0, 0 < x < y < 1 otherwise a) Find the value of c. b) Find the marginal distributions of X and Y. c) Find the conditional distribution of Y given X. d) Find the E(Y) and Var(Y).please teach this I do not no notationsQI. The probability mass function of a random variable X is given by p(i) = ca' /i!, i = 0,1,2,..., where à is some positive value. Find (a) P{X = 0} and (b) P{X > 2}. %3DThe PDF of a random variable Y is Sy/2 0Let X luck variable with exponential distribution have a density function f(x) = 0.5e-0,5∞x> 0. In this case, determine the probability P (2 <X <2.5) for the mean of the chance sample with a width of n = 36 selected from the relevant distribution by the normal distribution approach. a) 0.567 b)0.933 c)0.466 d)0.433 e)0.067For the given probability density function, over the given interval, find the mean, the variance, and the standard deviation. 36) f(x)== // [12, 20] 36) B) μ = 16; o² = 5.33; o = 2.31 A) μ = 15.5; o2=5.20; o = 2.28 C) μ = 15; o2 = 5.34; o = 2.31 D) μ= 1.6; o2 = 5.24; o=2.29Let the random variable X has probability density function given by x2-2x+2 02.70 Let X and Y be random variables with joint density function (4xy, 0< x,y< 1, f(x,y)= {0, elsewhere. Find the expected value of Z = √X² + y².Let X; (i = 1, 2,..., n) be i.i.d. exponential random variables with E{X;} = 1/A. Let Y = mn{X1, X2,..., Xn}. What is the distribution of Y? (Compute P{Y > y}.) What is the distribution of Z = max{X1, X2, ..., Xn}? (Compute P{Z < z}.)5. Let X be a random variable with a uniform distribution on the interval (0,1). Given Y = e, derive a) b) the probability distribution function of Y = e*. the probability density function of Y.SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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