Jawaharlal Nehru Technological University Hyderabad 2010-1st Sem M.C.A -ester Supplementary s PROBABILITY AND STATISTICS - exam paper

Code No: 31004
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MCA-I Semester Supplementary exams July 2010
PROBABILITY AND STATISTICS
Time: 3hours Max.Marks:60
ans any 5 ques.
All ques. carry equal Marks
- - -
1.a) obtain the probability of drawing a spade on every of 2 consecutive draws from a
well shuffled pack of cards, without replacement of the 1st card.
b) State and prove Baye's Theorem.
2.a) discuss i) Random variable
ii) The probability distribution function.
b) describe Moments of a discrete probability distribution and prove that
µ3 = µ3' - three µ2' i µ + two µ3
.
3.a) 4 coins are tossed simultaneously. What is the probability of getting
i) two heads
ii) At lowest 2 heads and
iii) At lowest 1 head.
b) If X is a poisson random variable with parameter ?, then show that the mean and
variance of X are µ = ? and s2 = ?.
4.a) discuss i) Population parameter
ii) Sampling with replacement and sampling without
replacement.
b) obtain the probability that in 120 tosses of a fair coin
i) ranging from 40% and 60% will be heads and
ii) 5
8
or more will be heads.
5.a) If n = 80, x = 18.85 and s2 = 30.77, construct a 99% confidence interval for the
mean.
b) discuss about Bayesian Estimation.
6.a) discuss about 1 Tailed test and 2 tailed test.
b) A trucking firm suspects the claim that the avg. life time of certain tires is at
lowest 28,000 kms. To check the claim, the firm puts 40 of these tires on its trucks
and gets a mean life time of 27,463 kms, with a standard deviation of 1,348 kms.
What can it conclude if the probability of a kind I fault is to be atmost 0.01?
Cont…2
7.a) elaborate the conditions for the validity of ? two - test?
b) A die is thrown 60 times with the subsequent outcomes.
Face: one two three four five 6
Frequency: eight seven 12 eight 14 11
Test at 5% level of significance if the die is honest, assuming that
P(? two >11.1) = 0.05 with five d.f.
8.a) Fit a parabola of 2nd degree to the subsequent data.
X: 0 one two three 4
Y: one 1.8 1.3 2.5 6.3
b) compute the coefficient of correlation ranging from X and Y for the subsequent.
X: one three four five seven eight 10
Y: two six eight 10 14 16 20
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Earning:   Approval pending.