Homework Answers

Find the global maximum and minimum values of the following function on the given interval. If there are multiple points in a single category list the points in increasing order in x value and enter N in any blank that you don't need to use.

f(x)=4e−x−4e−2x  [0,1]

Global maxima

x = ____ Y=___

x=_____ Y=____

x=____ Y=___

Global minima

x=____ Y=___

x=____ Y=___

x=___ Y=___

x=____ Y=___

12. To determine the weights of w1, w2 and w3 of three objects A1, A2 and A3, the following weighing

design was adopted. The objects were first weighed separately (A1 then A2 then A3) and then all

three (A1, A2 , A3) using ordinary two-parts balance. If the balancing weights in these four weighing

are denoted by x1, x2, x3 and x4 respectively with the expected values and variances given by

E(x1) = w1, E(x2) = w2, E(x3) = w3

E(x4) = w1 + w2 + w3

and

V ar(xi) = iσ2,

i = 1, 2, 3.

(a) By an appropriate method of estimating w1, w2, and w3, generate their normal equations and

present in a matrix form.

(b) Hence or otherwise, find the least square estimators of w1, w2, and w3 if V ar(xi) = iσ2,

i =

1, 2, 3.

(c) Given that x1 = 2.2, x2 = 1.7, x3 = 6.0, x4 = 9.5 and σ = 1.5, find the estimates for w1 and

w3.

8. Let (x1, x2, ..., xn) be independent measurements of a random variable X with density function

f(x) = e−(x−α), x > α. Find an estimator, ˆ

α, of α by method of moments.

STAT 333/Exx2

Solve the following LPPs using the simplex method

Max.Z=20x1 +10x2

Subject to:

5x1+4x2 < 250

2x1+5x2 < 150

x1, x2 > 0