Find the moment generating function for the random variable X whose density function is f(x). fx = 2x 0
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- Find the moment generating
function for the random variable X whose density function is f(x).
fx = 2x 0<x<1
MX(t) = _______________________________________
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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?A Troublesome Snowball One winter afternoon, unbeknownst to his mom, a child bring a snowball into the house, lays it on the floor, and then goes to watch T.V. Let W=W(t) be the volume of dirty water that has soaked into the carpet t minutes after the snowball was deposited on the floor. Explain in practical terms what the limiting value of W represents, and tell what has happened physically when this limiting value is reached.The 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)
- 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 below5. 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 Z2.4.6-3.) Random variables X and Y have respective density functions $x(x) = -[u(x) – u(x-a) to fy(y) = bu(y)e-by ob where a > 0 and b>0. Find and sketch the density function of W = X + Y if X and Y are statistically independent
- A random variable X has probability density function (pdf) fx(x), where fx(X)= c(1–x4) -1≤x≤1 i) Find cii) Find cdf Fx(x) of Xiii) Find the variance of X.iv)Find P [│X│ < 1/2]If the joint probability density function of two continuous random variables X and Y isgiven byf(x; y) = 2, 0 < y < 3x, 0 < x < 1; find(a) f(yjx),(b) E(Y jx),(c) Var(Y jx).A continuous variable Y has a probability density function for which the moment generating function is given by M(t)=e^(2*t+72*t^2). What is the variance of the variable, Var[Y]?
- Two random variables X and Y have a joint cumulative distribution function given by FXY(x, y) = 1/2 [u(x-2) + u(x-3)] {(1 – exp(-y/2)) u(y), then the marginal probability density function fx(x) is given byA random variable Y has a probability density function f(y) = A(y − 1.5) over the state space−2 ≤ y ≤ 3, where A is a constant. Calculate the median of the random variable Y.Your internal body temperature T in °F is a Gaussian (μ =98.6, σ = 0.4) random variable. In terms of the Φ function, find P[T > 100]. Does this model seem reasonable?
