Let X and Y be continuous random variables having a joint probability density function (pdf) given by f(x, y) = e-y, (i) (ii) (iii) 2|X = 3).
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- Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.Let X be a random variable with pdf: f(x)= k(10 - 2x) for x being [0,5] a.) Find k b.) Find E(X) c.) Find Var(X) d.) Find E(3 *squareroot(X))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 Y
- Let X and Y be independent random variables, prove that Var (XY) = Var (X) Var (Y) if E [X] = E[ Y] = 0.Let X be a random variable with pdf f(x) = kx*,-1C1. Let X be a continuous random variable with PDF f(x) = (2-x) ² for -1 1)? (c) Calculate the expectation of X. (d) Calculate the variance of X.Suppose that the random change in value of a financial asset is X over the first day and Y over the second. Suppose also that Var(X) =18 and Var(Y) = 26 In this case, the total change in the value over these two days is given by X +Y. Do you have enough information to compute Var(X +Y)? If so, compute this value. If not, explain what additional information you need to do so.C1. Let X be a continuous random variable with PDF f(x) = (2-x) for -1 ≤ x ≤ c and f(x) = 0 otherwise. (a) Explaining your work, find the value of the constant c. (b) What is P(X > 1)? (c) Calculate the expectation of X. (d) Calculate the variance of X.X is a continuous random variable and the pdf of X is k x> 1 f(x) xS 1 Determine the value of k for which f(x) is a legitimate pdf.Let X and Y be jointly continuous random variables with joint PDF cx +1, 2,y> 0, x+ y<1 0, fx,x (x, y) = otherwise. Then the constant c= And the probability that P(Y < 2X²) = ;: Here a = and b =F(x,y) = { (x+y)/42 ; x = 1,2,3 y = 1,2 0; elsewhere ] (i) Find the mean for the random variable X. (ii) Find the mean for the random variable Y. (iii) Find the covariance Cov[X,Y]A gasoline station gets its supply once a week. Suppose the PDF of X = demand in thousands of gallons for gasoline is: fx(x) = 5(1 – x)*I(0.1)(x) a. What is the probability that the demand for gasoline in a given week is more than 500 gallons? b. How much gasoline must the station get from its supplier in order for the probability that its supply will be exhausted in a given week shall be 0.01?SEE MORE QUESTIONS