Bharati Vidyapeeth 2007 B.E Biotechnology maths - Question Paper

distribution
x 0 one two three four five six 7
P(x) 0 k 2k 2k 3k k2 2k2 seven k2 + k
Find() ( ) ( 6) ( ) ( 6) i k ii PX iii P X < >
(b) If 10% of the rivets produced by a machine are defective, obtain the probability that, out of
12 rivets chosen at random.
(i) Exactly two will be defective (ii) Atleast two will be defective (iii)None of them be defective.
(c) Show that mean and standard deviation of exponential distribution are equal.
(7+7+6)marks
7. (a) discuss the subsequent terms
(i) Null hypothesis (ii) confidence limits (iii) kind I & II errors
(b) A die was thrown 9000 times and a throw of five or six was found 3240 times. On the
assumption of random throwing, do the data indicate that the die is biased?
(c) The weights of workers in a large factory are normally distributed with mean 68kgs and
S. D. three kgs. If 80 samples consisting of 35 workers every are chosen, how many of the 80
samples will have the mean ranging from 67 and 68.25 kgs?
provided (0 2) 0.4772 & (0 0.5) 0.1915 Pz P z £ £= £ £ = (7 + seven + 6)marks
8. (a) The joint distribution of 2 variables X and Y are provided below:
Y
X -4 two 7
1 1/8 1/4 1/8
5 1/4 1/8 1/8
Determine: (i) Marginal distributions of X and Y (ii) E(X) and E(Y).
(iii) Are X and Y independent random variables?
(b) describe Stochastic matrix. obtain a unique fixed probability vector for the regular Stochastic
matrix
0 three /4 one / 4
1 /2 one /2 0
0 one 0
æ ö
ç ÷
ç ÷
ç ÷
è ø
(c) 3 boys A, B & C are throwing a ball to every other. A always throws the ball to B and
B always throws the ball to C. But C is just as likely to throw the ball to B as to A. If C
was the 1st person to throw the ball, obtain the probabilities that (i) A has a ball (ii) B has
a ball (iii) C has the ball, for the fourth throw. (7 + seven + 6)marks

Visvesvaraya Technological University
Model ques. Paper – I
FOURTH SEMESTER B.E. exam ( 06BT-41)
NEW SCHEME
Biostatistics and Bio-modelling –IV
BIO-TECHNOLOGY
Time: 03 hours Max. Marks: 100

Earning:   Approval pending.