(7) Let X1,Xn are i.i.d. random variables, each with probability distribution F and prob- ability density function f. Define U=max{Xi , . . . , X,.), V=min(X1, ,X,). (a) Find the distribution functio...

Question

Question

(7) Let X1,Xn are i.i.d. random variables, each with probability distribution F and prob- ability density function f. Define

math Statistics-And-Probability

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

Varri abies each with DF F ond RDF (4) CDF amd PDF c)O P (smal test sample <u) valus {-P Cole sample >u) values = Tu b), at 2s amd s-th order statistic a oure ta it is demoted n-2)x

Add a comment

Answer 2

Similar Homework Help Questions

(5) Let X1,X2,,Xn be independent identically distributed (i.i.d.) random variables from 1.1 U(0,1). Denote V max{Xi,..., Xn) and W min{Xi,..., Xn] (a) Find the distributions and the densities and the...

(5) Let X1,X2,,Xn be independent identically distributed (i.i.d.) random variables from 1.1 U(0,1). Denote V max{Xi,..., Xn) and W min{Xi,..., Xn] (a) Find the distributions and the densities and the distributions of each of V and W. (b) Find E(V) and E(W) (5) Let X1,X2,,Xn be independent identically distributed (i.i.d.) random variables from 1.1 U(0,1). Denote V max{Xi,..., Xn) and W min{Xi,..., Xn] (a) Find the distributions and the densities and the distributions of each of V and W. (b)...
Let Ņ, X1. X2, . . . random variables over a probability space It is assumed that N takes nonnegative inteqer values. Let Zmax [X1, -. .XN! and W-min\X1,... ,XN Find the distribution function of Z...

Let Ņ, X1. X2, . . . random variables over a probability space It is assumed that N takes nonnegative inteqer values. Let Zmax [X1, -. .XN! and W-min\X1,... ,XN Find the distribution function of Z and W, if it suppose N, X1, X2, are independent random variables and X,, have the same distribution function, F, and a) N-1 is a geometric random variable with parameter p (P(N-k), (k 1,2,.)) b) V - 1 is a Poisson random variable with...
Central Limit Theorem: let x1,x2,...,xn be I.I.D. random variables with E(xi)= U Var(xi)= (sigma)^2 defind Z=...

Central Limit Theorem: let x1,x2,...,xn be I.I.D. random variables with E(xi)= U Var(xi)= (sigma)^2 defind Z= x1+x2+...+xn the distribution of Z converges to a gaussian distribution P(Z<=z)=1-Q((z-Uz)/(sigma)^2) Use MATLAB to prove the central limit theorem. To achieve this, you will need to generate N random variables (I.I.D. with the distribution of your choice) and show that the distribution of the sum approaches a Guassian distribution. Plot the distribution and matlab code. Hint: you may find the hist() function helpful

5. Let Xi i = 1,2, . ,N be i.i.d. U(0,1). Let Z = max{X1, .,Xn}...

5. Let Xi i = 1,2, . ,N be i.i.d. U(0,1). Let Z = max{X1, .,Xn} and find Fz.
Exercise 8.41. The random variables X1,..., Xn are i.i.d. We also know that ElXl] = 0. EĮKY = a and Elx?| = b. Let Xn-Xi+n+Xn. Find the third moment of Xn Exercise 8.41. The random variables X1,...

Exercise 8.41. The random variables X1,..., Xn are i.i.d. We also know that ElXl] = 0. EĮKY = a and Elx?| = b. Let Xn-Xi+n+Xn. Find the third moment of Xn Exercise 8.41. The random variables X1,..., Xn are i.i.d. We also know that ElXl] = 0. EĮKY = a and Elx?| = b. Let Xn-Xi+n+Xn. Find the third moment of Xn
7. Let X1, X2, ... be an i.i.d. random variables. (a) Show that max(X1,... , X,n)/n...

7. Let X1, X2, ... be an i.i.d. random variables. (a) Show that max(X1,... , X,n)/n >0 in probability if nP(Xn > n) -» 0. (b) Find a random variable Y satisfying nP(Y > n) ->0 and E(Y) = Oo

8. Let X1, X2,...,X, U(0,1) random variables and let M = max(X1, X2,...,xn). - Show that...

8. Let X1, X2,...,X, U(0,1) random variables and let M = max(X1, X2,...,xn). - Show that M. 1, that is, M, converges in probability to 1 as n o . - Show that n(1 - M.) Exp(1), that is, n(1 - M.) converges in distribution to an exponential r.v. with mean 1 as n .
Problem 2: Let Xi, X2,..., Xn be i.i.d. random variables with common probability density function 3...

Problem 2: Let Xi, X2,..., Xn be i.i.d. random variables with common probability density function 3 -6x21 (i) Calculate the MLE of 0 (ii) Find the limit distribution of Vn(0MLE - 0) and use this result to construct an approximate level 1-α C.I. for θ. [Your confidence interval must have an explicit a form as possible for full credit.] (iii) Calculate μι (0)-E0(Xi) and find a level 1-α C.İ. for μι (0) based on the result in (ii) or by...
4. Suppose that X1, X2, . . . , Xn are i.i.d. random variables with density function f(x) = 0 <...

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...

3. Suppose X1 with prob 1/2 and X-1 with prob. 1/2. Let Xi,.... Xn be i.i.d....

3. Suppose X1 with prob 1/2 and X-1 with prob. 1/2. Let Xi,.... Xn be i.i.d. with the same distribution as X (a) Find the mgf of X. (b) Let Ya=MtstAn. Find the mgfmyn(t). (c) Use the approximation: e 1for small r to find the liit of my (t) as noo for each fixed t. Can you identify this mgf?

(7) Let X1,Xn are i.i.d. random variables, each with probability distribution F and prob- ability density function f. Define U=max{Xi , . . . , X,.), V=min(X1, ,X,). (a) Find the distribution functio...

Homework Answers

Add Answer to:
(7) Let X1,Xn are i.i.d. random variables, each with probability distribution F and prob- ability density function f. Define U=max{Xi , . . . , X,.), V=min(X1, ,X,). (a) Find the distribution functio...

Post as a guest

Earn Coins

(5) Let X1,X2,,Xn be independent identically distributed (i.i.d.) random variables from 1.1 U(0,1). Denote V max{Xi,..., Xn) and W min{Xi,..., Xn] (a) Find the distributions and the densities and the...

Let Ņ, X1. X2, . . . random variables over a probability space It is assumed that N takes nonnegative inteqer values. Let Zmax [X1, -. .XN! and W-min\X1,... ,XN Find the distribution function of Z...

Central Limit Theorem: let x1,x2,...,xn be I.I.D. random variables with E(xi)= U Var(xi)= (sigma)^2 defind Z=...

5. Let Xi i = 1,2, . ,N be i.i.d. U(0,1). Let Z = max{X1, .,Xn}...

Exercise 8.41. The random variables X1,..., Xn are i.i.d. We also know that ElXl] = 0. EĮKY = a and Elx?| = b. Let Xn-Xi+n+Xn. Find the third moment of Xn Exercise 8.41. The random variables X1,...

7. Let X1, X2, ... be an i.i.d. random variables. (a) Show that max(X1,... , X,n)/n...

8. Let X1, X2,...,X, U(0,1) random variables and let M = max(X1, X2,...,xn). - Show that...

Problem 2: Let Xi, X2,..., Xn be i.i.d. random variables with common probability density function 3...

4. Suppose that X1, X2, . . . , Xn are i.i.d. random variables with density function f(x) = 0 <...

3. Suppose X1 with prob 1/2 and X-1 with prob. 1/2. Let Xi,.... Xn be i.i.d....

(7) Let X1,Xn are i.i.d. random variables, each with probability distribution F and prob- ability density function f. Define U=max{Xi , . . . , X,.), V=min(X1, ,X,). (a) Find the distribution functio...

Homework Answers

Add Answer to: (7) Let X1,Xn are i.i.d. random variables, each with probability distribution F and prob- ability density function f. Define U=max{Xi , . . . , X,.), V=min(X1, ,X,). (a) Find the distribution functio...

Post as a guest

Earn Coins

Add Answer to:
(7) Let X1,Xn are i.i.d. random variables, each with probability distribution F and prob- ability density function f. Define U=max{Xi , . . . , X,.), V=min(X1, ,X,). (a) Find the distribution functio...