A random variable X is uniformly distributed in (0, 6). If X is transformed to a new random variable Y = 2(X – 3)² – 4, find (i) the density of Y and
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- The weekly sales for a drinking water product (in 1000s of liters) is a continuous random variable Y with probability density function (pdf)f(y) v-1) 0Q 4.2. Let (X, Y) be a random variable with the following density: 15x²y 0 0 < x < y < 1, otherwise. fx,y(x, y) = { { 1. Express E(YX) in terms of X. 2. Express Var(X|Y) in terms of Y.Two independent random variables, X and Y, are both uniformly distributed on [0, 1]. The random variable Z is defined by Z = (X-H)² + (Y - My) ², E[X] and y E[Y]. Determine the expected value of Z. where (a) (b) = Determine the variance of Z.Let Ap and B be the random variables. A random process is defined a X () = Ag cos ont+ B sin ant, where og is a real constant. Find the power density spectru m of X (), if Ag and B, are uncorrelated random variables with zero mean and same variance.Consider a random variable Y with density S (1/2)(y + 1), -1 < y < 1, else. f(y) Calculate E(W) and V(W) for the random variable W = 4+Y – 2Y².4. Let X and Y be independent, continuous random variables with densities and fx(x) = = fy (y) = = 0 {} if 0 < x < 2 otherwise. y if 0Determine the marginal or density function and whether the random variables are independent.2 Find the conditional variance of X, given Y, where X and Y are random variables with the joint density fXY (x, y) =1 for 00 sr<1, 0Suppose X and Y are independent random variables. X iş uniformly distributed on (0,) and Y is exponentially distributed with 1=2. Find the joint density function f(x, y) of X and Y.X (f) = A cos on i+ B sin wn t, where on is a real constant. Find the power Let An and B, be the random variables. A random process is defined as density spectrum of X (t), if A, and Bo are uncorrelated random variables with zero mean and same variance.b) X-XN (0,1), and W₁ σχ YHYN(0,1), for i=1,2,3,...,10, then: Let Z₁ = i) State, with parameter(s), the probability distribution of the statistic, T = ay 10 ΣW2 √Σt,w₁² ii) Find the mean and variance of the statistic T = 10 Σ{12/2 iii) Calculate the probability that a statistic T = Z₁ + W₁ is at most 4. iv) Find the value of ß such that P(T> B) = 0.01, where T = E₁Z²+₁ W².Example 18.2 For the probability density of a system of random variables (X, Y): f(x, y) = 0.5 sin (x + y) (0 < x < 7,0 << 7), 2' determine (a) the distribution function of the system, (b) the expectations of X and Y, (c) the covariance matrix.SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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