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- If the prob density of a rv is given by f(x)=kx² 07. For a bivariate normal distribution with µx,µy,o} > 0,0² > 0 and |p| < 1, (a) Find the conditional density for X Y = y. (b) Determine the distribution of X² − 2pXY+Y² 1 - p² = 1. when μx = μy = 0 and o =Let X and Y be continuous random variables with joint p.d. f. f(x,y) = {* (12x for 0< y< 2x < 1 elsewhere The conditional density function of Y given X = x isi need the answer quicklySuppose that X and Y have a continuous joint distribution for which the joint probability den- sity function is defined as follows: fx.x (@, y) = { 3y² for 0≤x≤ 2 and 0 ≤ y ≤ 1 otherwise. (a) Determine P(X < 1,Y ≥ 1/2). (b) Determine the marginal probability density functions of X and Y. (c) Are X and Y independent? Explain.5.Suppose X is a continuous variable with density function (3,2 f(x) ={2" .-l5. 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.25. Let X and Y be continuous random variables with joint density function for 017. If a random variable X has the exponential distribution with density function f(x)= 2e* = 0, x>0 for x<0 What is the probability that X is not smaller than 2. Show that the coefficient of variation = 1.4. Let X, Y be jointly continuous with density f(x, y) = = c(x - y)e-2 File Preview (a) Find the value of c. (b) Find the conditional distribution of X|Y. 0 < x<∞, -x < y < x otherwiseaanswer: pleaseB1. Let us consider a random variable X following a Weibull distribution with parameter k = 2 and A > 0, which has density function Se-/A)", if x2 0, 0, fx(x) otherwise. Given the following random numbers sampled from the uniform distribution on the interval [0, 1], u1 = 0.1345, u2 = 0.7515, uz = 0.1671, u4 = 0.9101 and uz = 0.0578; compute five sampled values for X for A = 3.Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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