(10) Find Std(X) when X is a discrete random variable with the following given density. (i) f(z) = }, z = 6, 7, 8, 9, 10, (iii) f(x) = z = 1,2, … … · , n, where n = 100, ()(") (4) (vii) f(z) = 0.3(0.7)*, z = 0, 1, … . ', (ix) /(r) = , z %3D %3D (v) S(x) = -, # = 0, 1, 2, 3, (10 %3D = 1, 2, ...
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Answer only (vii), and (ix)
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- 8. Let the probability density of the random variable ({, n) be f(x, y) = { ke-(2x+7y) x>0 y>o elsewhere Find (1) the constant k; (2) the distribution function of (§, n);Let X and Y are 2 independent random variables N (0,1) Questions: how to find E(X), E(Y), E(X^2), E(Y^2)? Thank youLet X and Y be two continuous random variables with joint probability density (3x function given by: f(x.y)%= 0sysxLet X and Y are two random variables with p.d.f as F(x,y) = 3x^2y+3xy^2,0 < x< 1,0 < y < 1. (i) Find conditional density of X given Y. (ii) Find the mean, mode and standard deviation of r.v Y. (iii) Correlation between X and Y. (iv) Check that X and Y are independent or not?A random variable Y has a uniform distribution over the interval (8,, e,). Derive the variance of Y. Find E(Y)? in terms of (e,, e,). E(Y)? = Find E(Y) in terms of (e,, e,). E(Y) = Find V(Y) in terms of (8,, e,). V(Y) =Let X and Y be two random variables with joint probability mass function: p(x,y) = xy(1+y) for X=1,2,3 and Y=1,2 p(x,y) = 0, Otherwise. Please enter the answer to 2 decimal places. • What is the variance of (4-5X)?The density function of two random variables X and Y is ,-2(x+y) fx,r (x, y) =u(x)u(y)4e¯¾x*y) X,Y Find the mean value of the function e-*+),If X, Y are standardized random variables and 1+ 2ab a² +6²' r(aX+bY,bX+aY) = find r(X, Y), the coefficient of correlation between X and Y.2. Let X be a random variable with density function ) = √(2x² - + f(x) = Find the expected value of g(x) = 2X+1. 8x2 +5x + 6), 1 < x < 2, 0, elsewhereLet the joint density of random variables x and y be given by the following: fx,y(x, y) = 0.158(x + 1)8(y) + 0.18(x)8(y) + 0.18(x)8(y-2) +0.48(x - 1)8(y + 2) +0.28(x - 1)8(y-1) + 0.058(x - 1)8(y - 3) a) Determine the marginal density x and y of this joint density. b) Are these random variables statistically independent? Justify your answer. c) Find the marginal distribution functions for these random variables.Let X and Y be two continuous random variables with joint probability density (3x function given by: f (x.y)=D 0X is a discrete uniform (1,3) random variable. When X=x, Y is discrete uniform (1,x). (a) Find the correlation of X and Y (b) Find the mean value of X when Y=2.SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON