Prove the following: (a) E (C X) = Č E(X) (b) E (X + Y) = E(X) + E(Y) (c) E (XY) = E(X) · E(Y) When X and Y are statistically independent. %3D
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.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?What is your predicted average population growth rate from this method, in terms of lambda AND % per year? Does that predict an increasing or decreasing population, on average? Year (t) Nests at time t Nests at t + 1 N(t+1)/N(t) 1983 746 780 1.046 1984 780 702 0.900 1985 702 744 1.060 1986 744 729 0.980 1987 729 843 1.156 1988 843 905 1.074 1989 905 992 1.096 1990 992 1180 1.190 1991 1180 1275 1.081 1992 1275 1241 0.973 1993 1241 1566 1.262 1994 1566 1930 1.232 1995 1930 1915 0.992 1996 1915 2219 1.159 1997 2219 3482 1.569 1998 3482 3365 0.966 1999 3365 5834 1.734 2000 5834 4927 0.845 2001 4927 5525 1.121 2002 5525 7601 1.376 2003 7601 6446 0.848 2004 6446 9258 1.436 2005 9258 10899 1.177 2006 10899 average 1.142
- For b there are two cases and for c I have to plug the initial data into the odeLet X denote the temperature at which a certain chemical reaction takes place. Suppose that X has pdf f(x)={1/9(4-x^2) -1<=x<=2 0 otherwise a) Compute P(0≤ X ≤1)b) Obtain E(x) and Variance of XUse the expected value properties to obtain the E[Y] of the following system : y = 3x + 1 , where E[X] =3
- Let x~ possion(alpha). Show that E[x(x-1)(x-2)....(x-k)]=ak+1Prove that the mean and variance are obtainablefrom RX(t)= ln(MX(t)): MEAN=E(X)=Rx'(0), VARIANCE=V(X)=Rx''(0),For an exponential random variable (X) having θ = 4 and pdf given by: f(x) = (1/θ)e^(−x/θ ) where x ≥ 0, compute the following: a) E(X). b) Var(X). c) P(X > 3).
- f X1,X2,...,Xn constitute a random sample of size n from a geometric population, show that Y = X1 + X2 + ···+ Xn is a sufficient estimator of the parameter θ.1. Find the population covariance between X and Y .2. Find E[Y |X = x].3. Find Var[Y |X = x].Which of the following processes (Xt)t is weakly stationary? A: Xt = 1:6 + Xt 1 + V tB: Xt = 0:6 Xt-1 +V tC: Xt = 0:8 Xt-1 + V tD: Xt = 0:8 t + 0:6 V t – 1 The term (t) is always assumed to be white noise with variance one