Let X(t) =
2; if 0 t 1;
3; if 1 t 3;
-5; if 3 t 4:
or in one formula X(t) = 2I[0;1](t) +
3I(1;3](t) -
5I(3;4](t).
Give the Itˆo integral
X(t)dB(t)
as a sum of random variables, give its distribution,
specify the mean and the variance.
Let X(t) = 2; if 0 t 1; 3; if 1 t 3; -5; if 3 t 4: or in one formula X(t) = 2I[0;1](t) + 3I...
Let S ⊆ be the tetrahedron having vertices (0, 0, 0), (0, 1, 1), (1, 2, 3), and (−1, 0, 1). Let f : → be the function defined by f(x, y, x) = x − 2y + 3z. Using the change of variables theorem, rewrite as an integral over a 3-rectangle, then use Fubini’s theorem to evaluate the integral. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image}
Let X1,...,X10 be a random sample from N(θ1,1) distribution and let Y1,...,Y10 be an independent random sample from N(θ2,1) distribution. Let φ(X,Y ) = 1 if X < Y , −5 if X ≥ Y , and V= φ(Xi,Yj) . 1. Find v so that P[V>=v]=0.45 when 1=2. 2. Find the mean and variance of V when 1=2. 10 10 2 We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe...
.........,, random sampling of the normal distribution of the unit n, and and ile -1 Let the sample mean and sample variance be respectively. a) b) ile -1 it is independent. c) d) What is the proof ?? We were unable to transcribe this imagen Ν(μ, σ2) T We were unable to transcribe this imageWe were unable to transcribe this imageT We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable...
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...
Let two variables and are bivariately normally distributed with mean vector component and and co-variance matrix shown below: . (a) What is the probability distribution function of joint Gaussian ? (Show it with and ) (b) What is the eigenvalues of co-variance matrix ? (c) Given the condition that the sum of squared values of each eigenvector are equal to 1, what is the eigenvectors of co-variance matrix ? please help with all parts! thank you! X1 We were unable...
Let X be a random variable from a distribution with density . Calculate the variance of random variable We were unable to transcribe this image3.22 +1
Let X1,X2,...,Xn denote independent and identically distributed random variables with variance 2. Which of the following is sucient to conclude that the estimator T = f(X1,...,Xn) of a parameter ✓ is consistent (fully justify your answer): (a) Var(T)= (b) E(T)= and Var(T)= . (c) E(T)=. (d) E(T)= and Var(T)= We were unable to transcribe this imageWe were unable to transcribe this imageoe We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this...
Let X ~ Poisson(). Show that as , converges in distribution to a random variable Y and find the distribution of Y. We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
1. Let X be a discrete random variable with a cumulative distribution function: a. Use this cdf to fin the limiting distribution of the random variable when with , as n increases. Use the fact b. What kind of random variable is for large value of n? We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imagep= We were unable to transcribe this imageWe were unable to transcribe this imageWe were...
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...