Derive the moment generating function of y= a x1+b x2,
where y~ N( a 1 + b2 , a2 12 +b222 + 2ab cov(x1, x2) ), not both a and b equal to zero.
Derive the moment generating function of y= a x1+b x2, where y~ N( a 1 +...
Suppose Y-X1-X2 where X1, x2 are iid Poisson(11) (a) Show that Y has moment generating function My (t) = e11(ette-t-2) (b) Even though you can do it from other results, use the mgf in (a) to find Var(Y).
Suppose we have 5 independent and identically distributed random variables X1, X2, X3, X4,X5 each with the moment generating function 212 Let the random variable Y be defined as Y = Σ We were unable to transcribe this image
9 Let Xi, X2, ..., Xn be an independent trials process with normal density of mean 1 and variance 2. Find the moment generating function for (a) X (b) S2 =X1 + X2 . (c) Sn=X1+X2 + . . . + Xn. (d) An -Sn/n 9 Let Xi, X2, ..., Xn be an independent trials process with normal density of mean 1 and variance 2. Find the moment generating function for (a) X (b) S2 =X1 + X2 . (c)...
Let X1, X2,.......Xn be a random sample of size n from a continuous distribution symmetric about . For testing H0: = 10 vs H1: < 10, consider the statistic T- = Ri+ (1-i), where i =1 if Xi>10 , 0 otherwise; and Ri+ is the rank of (Xi - 10) among |X1 -10|, |X2-10|......|Xn -10|. 1. Find the null mean and variance of T- . 2. Find the exact null distribution of T- for n=5. We were unable to transcribe this imageWe were...
Let X1, X2, X3 ∼(iid) Exponential(λ). (a) Show that T(X1, X2, X3) = X1 + X2 + X3 is a sufficient statistic for λ. (b) Find the MVUE for λ. (c) Show that is not a sufficient statistic for λ. (d) Let = and find . Give an argument for why is not the best estimator of λ. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to...
and are independent what is the distribution of Y=X1+X2 X~ bin(n,p) We were unable to transcribe this image
4. Suppose that X1, X2, . . . , Xn are i.i.d. random variables with density function f(x) = 0 < x < 1, > 0 a) Find a sufficient statistic for . Is the statistic minimal sufficient? b) Find the MLE for and verify that it is a function of the statistic in a) c) Find IX() and hence give the CRLB for an unbiased estimator of . pdf means probability distribution function We were unable to transcribe this...
Wanting help with part (b) a) Derive the moment generating function (m.g.f) of the triangular distri- bution Y with p.d.f 0elsewhere Hint: Use Integration by parts. (b) Determine the moments Y by expressing it as a Taylor series, i.e. identify the corresponding coefficients Note: Since EY-0, the kth moment is the kth central moment (c) Determine the m.gf. of U-μ + bY. [Note: μ 0 is an unspecified constant here, it is not the mean of Y which is zero.]...
Let X1, X2, ..., Xn be a random sample from X which has pdf depending on a parameter and (i) (ii) where < x < . In both these two cases a) write down the log-likelihood function and find a 1-dimensional sufficient statistic for b) find the score function and the maximum likelihood estimator of c) find the observed information and evaluate the Fisher information at = 1. f(20) We were unable to transcribe this image((z(0 – 2) - )dxəz(47)...
Let X be N(0, 1), derive the moment generating function of X