d. Standard deviations of X and Y e. Correlation, E(XY) f. Covariance, Cov(X, Y) g. Correlation coefficient
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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?ASAP!Random variables! K=1/22000... where k is constant of given function of x and y.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 + 2Y
- 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 = X2T=X³, V=2Y²-3Y+4 Calculate the covariance by creating a common distribution table for the given random variables (T,V) .the random variable Y is such that : E(2Y+3)=6 and Var(2-3Y)=11 find E(Y^2)
- Salinity in Quebec river is a combination of tides and rain. Rain that diluted the salt occurs about 10% of the time, while the non salty outgoing tides occurs twice per day. You take your dog for a walk down by the river at random during the weekend and notice that he'll drink from the river 30% of the time when the salt is sufficiently low. someone points out that the saltiness doesn't depend on the local rain but on the rain upriver. Assume that at any time it is possible to have 3 independent rainstorms upriver , all with the same 10% probability of occurrence that you see at the city. What is the probability of no rain upriver ? Of 1 rain ? Of more than one ? please tell which probability formula you useSolve 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.Let X and Y be independent random variables with E[X]=3, E[X^2] =25 E[Y] = 10 , E[Y^2] = 164 (d) Find Var(Y).(e) Find Var[3X + Y - 8].
- T=X³, V=2Y²-3Y+4 Calculate the covariance by creating the common distribution table for the random variables given above. COV(T,V)X1 ∼ N(µ, σ2) ve X2 ∼ N(µ, 3σ²)Let them be independent random variables. X¯ = (X1 + X2)/2 be defined as. a) Calculate the variance of X¯. B) α ∈ [0, 1] i¸cin ˜µ = αX1 + (1 − α)X2 be defined as.µ is an unbiased estimate of µ is it? Prove your answer. C) Calculate the variance of µ.A continuous random variable X has the PDF fx(x)=kx2, 0 < ? < 1.a) What is the value of k ?b) Find the variance of Xc) What is the value of m so that P[X<=m] = 1/2 ?d) Find the PDF of the new random variable Y obtained from X through the lineartransformation Y=4X+1.
