FINA 6281 Assignment 1 - Word VIEW NITRO PRO 10 AaBbCcDa AaBbCcI AaBbCcI AaBbCcDd AaBbCc] AaBbCc] AaBbCcI AaBbCcDd AaBbCcDd AaBbCcDI A Heading 2 1 Heading 3 1 Heading 4 1 Heading 5 1 Heading 6 1 List Para. Normal Strong Empha Heading 1. (Probability) (a) The variance of a random variable X may be denoted as: var (X) - = [( X - E(D)" how that this may also be written as Var(X) - E[X ] - (E[XD (b) The covariance of two random variables Xand Y'may be denoted as Cov(X. Y) - =[(x - .)(r - 2,)] show that this may also be written as Cov (X. Y) = E[XY] - Hcky- (c) If two random variables Xand Yare uncorrelated then (multiple choice question) 1. Cov(X, Y) = 0; 2. X and Yare independent: 3. E[XY] = 0; 4. None of the above. (d) Suppose that the CDF of a random variable Find the PDF. Hint: the PDF is the derivative of the density f (x) = F(x)). -) Show that f (x, y) = 27 evaluate to one) by evaluating: function ( should (f) Given the following cumulative distribution function (CDF), F(x), for 0 s x s 10; F (x ) - x 106 (20 - x) Check that this is a valid CDF (i.c. show that F(0) - 0 and F(10) - 1) and calculate the probability density function. f(x)