1. .. .
PART B - (5 x 16::: 80 marks)
11. (a) Explain different types of Fuzzy quantifiers with suitable examples. (16)
"
Or "'-,
(b) (i) What type of operators are used in )'uzzy expressions? (8)
(8)(ii) What are the four valued logic and its uses?
12. (a) Construct QR decomposition for the matrix
0 1 1 1
1 0 1 1
A=
1 1 0 1
1 1 1 0
(16)
Or
value decomposition for the matrix
(16)
13. (a) (i) IfX represents the outcome, when a fair die is tossed, find the .MGF
of X and hence find E(X) and Var(X). (6)
(ii) If X and Y are independent RVs with pdf's e-x, x ~ 0 and
e-Y
, y ~ 0, respectively, find the density functions of U = X
X+Y
and V =X +Y . Are U and V independent? (10)
Or
(b) (i) Find the MGF of the binomial distribution and hence find its mean
and variance. (8)
(ii) The time (in hours) required to repair a machine is exponentially
distributed with parameter It:::; 1...
2
(1) What is the probability that the repairs time exceeds 2 hour?
(2) What is the conditional probability that a repair takes 10 hour
given that its duration exceeds 9 hour? (8)