Question

Q7). Let y,,y.., y represent the life time for the computer chips that are exponentially distributed with pdf e^ for else (a). Derive the likelihood ratio test for testing Ho: λ A, versus Ha: λ> λ (b). If a random sample of life times for the computer chips are 4 years, 5 years, 7 years, 6 years, 7 years, Use α-005 does this sample support the fact that λ > 4.5 years ?. 4.6, 4.7, 4.8, 4.9, 5.0 Compute the power of the test at λ (c). (10 points) Q6). Suppose that you want to fit two separate regression lines on the same data set , xn,y - For the first least square fit, Y is the response variable and X is the predictor variable - For the second least square fit, X is the response variable and Y is the predictor variable Show that the product of the slope estimates from the two regression lines is (a). Show that the above two regression lines will never be perpendicular to each other (b). (20 points)

Answer 1

6)

a)

when Y is regressed on X

then slope =

Cov(X, Y) mi = Var(X

when X is regressed on Y

Cov(X, Y) m2 =-Var(Y)

product =

Cov(X, Y) Cov(X, Y) mmVarX) Var(Y

$Cov(X,Y) = \frac{\sum (X_i - \overline{X})(y_i - \overline{Y})}{n-1}$

Var(X)

Var(Y)-n

hence

m1 m2 is same as shown in image

b)

here m1m2 >= 0

for perpendicular

m1 m2 should be -1

hence two lines will never be perpendicular

Please post Q7 again