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- C1. Let X be a continuous random variable with PDF f(x) = ? (2 – a) for –1 1)? (c) Calculate the expectation and variance of X. (d) Let Y (X2 – 1). What is the expectation of Y?X is a random variable with distribution X 1 P(x) 0.4 0.6 X1 and X2 are two random variables and both have the same distribution as X. Let Y = X1 - X2. Find the distribution of Y. Y = 0 Y -1 1 P(y) 0.25 0.50 0.25 Y -1 1 P(y) 0.24 0.52 0.24 Y 1 2 P(y) 0.16 0.48 0.36Q1. Let X; and S be the mean and variance of independent random samples of size ni from populations with mean H; and variance of (i = 1,2), respectively where u, = 20. of = 9, n1 = 36 and u2 = 18, ož = 16, n2 = 49. Find (- a) P(X, > 20.98) b) x such that P(X, 12.8062) d) si such that P(S} > s3) = 0.80 e) P(X1 – X2 > 0.2336) n P(SE/S글 > 0.8368) %3D
- 3) Suppose X is a discrete variable that has the following pr function (pdf) f (X) 1. 0.40 0.20 3 0.15 4. 0.25 a) Calculate the cumulative distribution function (the b) Find the expected value, showing your work: E(X) c) Find the variance, showing your work: Var (X)12. i. State Central limit theorem and tell what is the main theme of it. ii. Show that if the random variables (X, Y) follow the probability density of a bivariate normal distribution and if the correlation p = 0, X and Y are independent. (Show that f(x, y) = g(x) h(y))A4. If random variables X and Y each have variance o? = 3 and corr(X,Y) = 0.4, what is the value of Cov(3X – 1, 2Y + 2)?
- Q1. let Y₁ < Y₂ < Y3 < Y4 < Y5 are the order statistics of the random sample of size 5 from the distribution : f(x) = 3x², 02. The random variable X is the amount of fructose in apples (in ounces) grown at a local orchard and is represented by the following cdf: 2(x +), 13. Let the random variable X have the moment generating function M(t) = What are the mean and the variance of X, respectively? -1 < t < 1.Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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