If the PDF of X is f(x)=2x/k2 for 0
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If the
PDF of X is f(x)=2x/k2 for 0<x<k, for what value of k is the variance of X equal to 2?
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- Let 0, X,, X2,... be RVs. Suppose that, conditional on = 0, X1, X2, ... are independent and X, is normally distributed with mean 0 and variance o. Suppose that the marginal PDF of O is 1 T(0) = e 0ER. Calculate the mean and variance of O conditional on X, =x, ..., X,= x„.Let X ~ U[0,1] and Y = -βln(1-X). What is the distribution of Y? Justify.5. Find the moment generating function of the exponentially distributed random vari- able with pdf Xe-, x≥0 and use it to evaluate the mean and variance of X.
- Example 10: Show that r = where r= coefficient of correlation 20,0, between x and y, ,0,,0+) are the variances of x.y and x+ y respectively.-Ar 45. First three moments of a variable measured by point "2" are 1, 16 and - 40. Prove that mean is 3, variance is 15 and u4 = -86.IF it was XG (23) Independent of Xen G (13) Find Miley D-Probability density Function of the Variable YaX+Xq 2 -the Mean variance of the variable
- Suppose you just bought one share of stock A and want to hedge it by shorting stock B. How many shares of B should you short to minimize the variance of the hedged position? Assume that the variance of stock A's return is o?; the variance of B's return is o?; their correlation coefficient is p. Please show your derivation by attaching a file below. Hint: 1. we don't restrict the solution to be an integer, it can be a non-negative value 2. we don't set constraints for the target returnThe Regression Coefficients from a fitted Bass Model were A =400, B= 0.088, C= -0.00000045. What is the estimated market potential for this product category? Select one: a. 200,000 b. 125,000 c. 800,000 d. 580,000Suppose X = number of direct injuries occurring in a fire incident. Its PMF is given by x 0 1 2 3 4 5 6 7 f(x) 0.08 0.08 0.09 0.14 0.18 0.18 0.16 0.09 0.06 Determine the mean and variance of the number of direct injuries occurring in a fire incident. 8 0.06
- Each day a random number, N ,of visitors make a purchase. The mean of N is E(N) = 12.8 and its variance is V(N) = 8.5 %3| Each of these visitors independently from the others spends a random amount of money, X; with mean E(X;)= 130.0 and variance V(X;) = 42.0 Let Y Σ Χ a day. be the total amount of money spent by visitors in the shop in Find the mean of Y and the variance of YCalculate the Average and the varianceShow that the serial correlation coefficient p is equal to -1, if n = 2, provided the denominator is not zero.
