## Compute the corresponding normal approximations

This is a binomial random variable…n = 20p = 0.5q = (1-p) = 0.5Compute the corresponding normal approximations with thecontinuity correction for P(8

## How large can the power possibly be?

Consider two probability density functions on[0,1]: f0(x)=1, and f1(x)=2x.Among alltests of the null hypothesisH0: X~f0(x)verses the alternative X~f1(x), with significance levelα=0.10, how large can the power possibly be?

## JOINT PROBABILITY

3.62 THE JOINT PROBABILITY DENSITY FUNCTION OF THE RANDOM VARIBLE X, Y, AND Z IS:f(x,y,z) = {4xyz^2/9,0 1/3, 1< Z<2);d.) P(0

## Joint density function

The joint density function of Y1 and Y2 is given by

f(y1,y2) = { 30y1y22,(y1- 1) 21) , 0 1

0, otherwise

a.Find F(1/2, 1/2).

## Find

Let X1,X2,…,Xn be independent, uniformly distributed random variables on the interval [0,θ].

Find the c.d.f. of Yn=max(X1,X2,…,Xn).

## Compute the dual prices for the three constraints.

The optimal solution of the linear programmingproblem is at the intersection of constraints 1 and 2.

Max2x1+x2

s.t.4×1+ 1×2 400

4×1+ 3×2 600

1×1+ 2×2£ 300

x1 , x2 >0

Compute the dual prices for the threeconstraints.

.45, .25, 0
.25, .25, 0
0, .25, .45
.45, .25, .25

## Derive

Let X1,…,Xn be a random sample from aNB(3,p) distribution with mean and varianceμ = EX1 = (3(1-p))/(p)σ2 = VarX1 =(3(1-p))/(p2).Derive the MLE’s of μ and σ2.

## Find the joint distribution function

LetX1,X2 have the jointpdf f(x1,x2)= 1/π for 0 21 + x22 1; 0 elsewhere. Find the joint distributionfunction G(t1,t2) =P(T1 t1;T2 t2) ofT1 = X21 +X22 ,T2 = X2by thedistribution function method, for 0 t11; 1 ·2 1 and hencethemarginal distribution function of T1 asG1(t1) = G(t1;t2 =√t1):

From my class examples I tried to take the double integral but donot know the intervals of each integral dx1,dx2 . Do I need to take polarcoordinates? Or do Iuse x11-t22) andx21 for theinterval? Cananybody direct me to the correct place?? Myteacher says “in the double-integral forP(X1^2+X2^2 “