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- If X is exponentially distributed with parameter λ and Y is uniformly distributed on the interval [a, b], what is the moment generating function of X + 2Y ?A rectangular plate with insulated surface is 10 cm. wide and so long compared to its width that it may be considered infinite length. If the temperature along short edge y = 0 is given u(x,0) = 8 sin(px/ 10) when 0 <x <10, while the two long edges x = 0 and x = 10 as well as the other short edge are kept at 0o C, find the steady state temperature distribution u(x,y).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.
- In an effort to make the distribution of income more nearly equal, the government of a country passes a tax law that changes the Lorenz curve from y = 0.98x2.1for one year to y = 0.32x2 + 0.68x for the next year. Find the Gini coefficient of income for both years. (Round your answers to three decimal places.) after beforea) Find the marginal pmfs of X and Y b) Find the conditional pmf of X given Y = 1Show mathematically that MRS is increasing for U=1-ex +e2y and is diminishing for U=lnX +LnY
- 4.) Suppose X has moment generating function MX(t) = 0.3e−t + 0.1 + 0.1et + 0.2e2t + 0.3e3t. What is P(X = 2)? What is the P(X = −1)? (To do this problem think about the definition of MX(t) as E(etX) = Σ ext P(X = x)).df between = df within = F Critical = SS Between = SS within = MS between = MS within = F = R^2= Fail to reject the null or reject the null hypothesis?5. Klein is located on the tangent line to y=3x2 -x at x = 1.