Let X and Y be jointly continuous random variables with joint PDF is given: f X,Y (x.y) (1+x²y) tco,l) a) I co,2) Cy)
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- b) Let Z₁-N(0,1), and W₁ = Y~N(0,1), for i=1,2,3,...,10, then: dx dy i) State, with parameter(s), the probability distribution of the statistic, T = - 154 ii) Find the mean and variance of the statistic T = ₁² 10 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 = ₁2₁² +².let X and Y be a random variables having pdf f(x,y)=2xy 0<x<y<1 Find P(X/Y<1/2)Let random variables X and Y have the joint pdf fX,Y (x, y) = 4xy, 0 < x < 1, 0 < y < 1 0, otherwise Find the joint pdf of U = X^2 and V = XY.
- Let X and Y continuous random variable with joint pdf fx,y) = 24xy, for 02. Let X and Y be jointly continuous random variables with joint PDF x + cy2 0, OSXS1,0Sys1 elsewhere a) Find the constant c Find the marginal PDF's fy(x) and fy(y) c) Find P(OSXS1/2,0SYS1/2) b)Let X1, X2,... , Xn be independent Exp(A) random variables. Let Y = X(1)min{X1, X2, ... , Xn}. Show that Y follows Exp(nA) dis- tribution. Hint: Find the pdf of YLet X and Y be continuous random variables having a joint pdf given by f(x, y) = e-*, 0sysx 3).Let X and Y be two independent random variables each uniformly distributed over (0, 1). Find the joint pdf of R = VX² + Y²; 0 = tan-1G).b) Let Z₁ = X-XN (0,1), and W₁ dx YHY~N(0,1), for i = 1,2,3,...,10, then: dy i) State, with parameter(s), the probability distribution of the statistic, T = - 54 1² ii) Find the mean and variance of the statistic T = Σ},wp? Σ1,2,3 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 = Σ₁Z₁² + ₁ W₁².2. Let X and Y be jointly continuous random variables with joint PDF x + cy2 0, OSXS1,02. Let X and Y be jointly continuous random variables with joint PDF x + cy2 fy(X.v) = OsxS1,0Sys1 elsewhere la) Find the constant c b) Find the marginal PDF's fx(x) and fy(y) c) Find P(OSXS1/2,05YS/2)Q1) Discrete joint variables X and Y with probability density f(x,y) (pdf) are given in this table. Find: 1) The Covariance Cov(X,Y)? (Cov(X,Y) = MxY-MxMY) 2) The correlation (pxy) between X and Y where Pxy = Cov(X,Y) PXPY Y 3 fx(x) f(x,y) 1 2 1 1/4 1/4 0 X 2 0 1/4 1/4 fy(y) Note that 2 n=2 n=3 Px² = Σn²±²x² f(x, y) - μ and py² = Σ3y² f(x, y) – µ Zk=0SEE MORE QUESTIONSRecommended textbooks for youAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage