Question 1

2 Points

Given f(x,y)= 8xy, when 0<=x<=1, 0<=y<=x and f(x,y)=0 elsewhere, find

(i) Marginal density of x

(ii) Marginal density of y

(iii) Conditional density of x

(iv) Conditional density of y

Question 2

2 Points

Calculate the regression coefficients from the following :

Question 3

2 Points

Compute the rank correlation co-efficient for the following data:

Question 4

2 Points

 12 entries in a painting competition were ranked by two judges , Judge I : 5, 2, 3, 4, 1, 6, 8, 7, 10, 9, 12, 11 and by  Judge II: 4, 5, 2, 1, 6, 7, 10, 9, 11, 12, 3, 8 . Calculate Spearman’s rank correlation coefficient.

Question 5

2 Points

A manufacturer claims that only 4% of his products supplied by him are defective. A random sample of 600 products contains 36 defectives. Test the claim of the manufacturer.