Obtain (i) P (X < 1) (i) Р (тоd X > 1)
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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?5. Suppose Z is a Gaussian random variable with mean 0 and 1. (a) Find the moment generating function of Z2. (b) Find the density function of Z2.9.19 Let X and Y be two continuous random variables, with joint proba- bility density function f(x, y): - 30 -50x²-50y² +80xy for -
- 7)Let X1, X2, ..., Xn be a sample of n units from a population with a probability density function f (x I θ)=θxθ-1 , 0<x<1, θ>0 . According to this: X~ f (x I θ) . Find the distribution function of the random variable X.X1 and X2 are two discrete random variables, while the X1 random variable takes the values x1 = 1, x1 = 2 and x1 = 3, while the X2 random variable takes the values x2 = 10, x2 = 20 and x2 = 30. The combined probability mass function of the random variables X1 and X2 (pX1, X2 (x1, x2)) is given in the table below a) Find the marginal probability mass function (pX1 (X1)) of the random variable X1.b) Find the marginal probability mass function (pX2 (X2)) of the random variable X2.c) Find the expected value of the random variable X1.d) Find the expected value of the random variable X2.e) Find the variance of the random variable X1.f) Find the variance of the random variable X2.g) pX1 | X2 (x1 | x2 = 10) Find the mass function of the given conditional probability.h) pX2 | X1 (x2 | x1 = 2) Find the mass function of the given conditional probability.i) Are the random variables X1 and X2 independent? Show it. The combined probability mass function of the random variables X1 and X2 is belowThe density of a random variable X is f(x) = C/x^2 when x ≥ 10 and 0 otherwise. Find P(X > 20).
- Let X1, X2, ... , Xn be independent random variables where Xi ~ Poisson(λi) for i = 1, 2, ... , n. Find the moment generating function of Σi=1n Xi and find the pdf of X1 | Σi=1n Xi = kThe joint probability density function of two random variables X and Y is f(x, y)= 4xye^-(x^2+y^2). Find P(1<x<=2, 1<Y<=2)(a) Let Y1 , Y2 , · · · , Yn be independent and identically distributed random variables. Show if Y1 < Y2 is independent of the event Y1 < Y3.(b) Let Y1 , Y2 , · · · , Y∞ be dependent random variables with following probability density function; Yn+1 =3Yn with probability 1/3Yn+1 =Yn/3 with probability 2/3 for n ∈ [0, ∞) where Y0 = 1. Compute E[Y1] and E[Y2].
- Suppose that the random variables X, Y , and Z have the joint probability density function f(x,y,z)=cxyz for 0 < x < 1, 0 < y < 1, and 0 < z < 1. Find the E(x). Use the Scientific Method of Answering (Given, Required, Formula and Solution.)2)Let X1, X2, ..., Xn be a sample of n units from a population with a probability density function f (x I θ)=θxθ-1 , 0<x<1, θ>0 . According to this: Find the maximum likelihood estimator (MLE) of parameter θ.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
