Random variables X and Y have the joint PMF with a constant k P(x, y) = {kxy, X = 1,4; y = 1,3 otherwise
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- Altmans z-score Altmans z-score is a financial tool for predicting insolvency in a business. For a certain company, the z-score formula is z=0.84+0.6StockpriceOutstandingsharesTotalliabilty In this exercise, we assume that thre are 45, 000 outstanding shares at a price of 4.80 each. a. Use L, for total liability, in dollard, and give a formula for the z-score for this company. b. Would a larger total liability idicate a better or worese outlook for the company? c. A z-score of 1.81 or lower indicates a high probability of insolvency. What is the smallest value of L that will give a z-score that indicates a high probability on insolvency?X is the Gaussian (μ=1, σ=2) random variable. Y is the Gaussian (μ=2, σ=4) radnom variable. X and Y are independent. a) What is the PDF of V = X + Y b) What is the PDF of W = 3X + 2Y2. Y1, Y2, ..., Yn are i.i.d. exponential random variables with E{Yi} = 1/θ. Find thedistribution of Y =1 nPiYi.
- e random variable X has pdff(x) = (3x2/2, −1 < x < 1;0, otherwise.(a) Find the pdf of Y = |X|.(b) Find the pdf of Z = X2ASAP!Random variables! K=1/22000... where k is constant of given function of x and y.A derived random variable Y = 5X2 – 3 A random variable X with probability mass function Px(x) = 1/4 (for x =1, 2, 3, 4) and 0 elsewhere. a) Set up the CDF FY(y) in terms of CDF FY(x)b) Find the PMF PY(y) of the derived random variable Y
- A derived random variable Y = 5X2 – 3 A random variable X with probability mass function Px(x) = 1/4 (for x =1, 2, 3, 4) and 0 elsewhere. a) Set up the CDF FY(y) in terms of CDF FY(x) b) Find the PMF PY(y) of the derived random variable YLet X and Y be jointly distributed random variables. This exercise leads you through a proof of the fact that −1 ≤ ρX,Y ≤ 1. a) Express the quantity V(X − (σX/σY)Y) in terms of σX, σY, and Cov(X, Y). b) Use the fact that V(X − (σX/σY)Y) ≥ 0 and Cov(X, Y) = ρX,YσXσY to show that ρX,Y ≤ 1. c) Repeat parts (a) and (b) using V(X + (σX/σY)Y) to show that ρX,Y ≥ −1.Solve using the moment-generating function technique. Let X1, . . . , Xn be independent random variables, such that Xi ∼ N(µi, σ2) for i = 1, . . . , n. Find the distribution of Y = a1X1 + · · · + anXn.
- 13) Random variables X and Y have joint pdf fXY={4xy, 0≤x≤1, 0≤y≤1fXY={4xy, 0≤x≤1, 0≤y≤1 Find Correlation and CovarianceE(Yn)? Let X1,X2,... be a sequence of identically distributed random variables with E|X1|<∞ and let Yn = n−1max1≤i≤n|Xi|. Show that limnE(Yn) = 0 and limnYn =0a.s.Two random variables X and Y with a joint PDF f(x,y) = Bx+y for 0≤ x ≤6 , 0≤ x ≤7 and constant B Find value of constant B
