Code No: 31004
Time: 3hours Max.Marks:60
Answer any Five questions
All questions carry equal Marks
1.a) Find the probability of drawing a spade on each of two consecutive draws from a well shuffled pack of cards, without replacement of the first card.
b) State and prove Baye's Theorem.
2.a) Explain i) Random variable
ii) The probability distribution function.
b) Define Moments of a discrete probability distribution and prove that µ3 = µ3' - 3 µ2' i µ + 2 µ3
.
3.a) Four coins are tossed simultaneously. What is the probability of getting
i) 2 heads
ii) At least two heads and
iii) At least one 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) Explain i) Population parameter
ii) Sampling with replacement and sampling without
replacement.
b) Find the probability that in 120 tosses of a fair coin
i) between 40% and 60% will be heads and
ii) 58 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) Explain about Bayesian Estimation.
6.a) Explain about One Tailed test and two tailed test.
b) A trucking firm suspects the claim that the average life time of certain tires is at
least 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 Type I error is to be atmost 0.01?
Cont…2
7.a) What are the conditions for the validity of ? 2 - test?
b) A die is thrown 60 times with the following results.
Face: 1 2 3 4 5 6
Frequency: 8 7 12 8 14 11
Test at 5% level of significance if the die is honest, assuming that
P(? 2 >11.1) = 0.05 with 5 d.f.
8.a) Fit a parabola of second degree to the following data.
X: 0 1 2 3 4
Y: 1 1.8 1.3 2.5 6.3
b) Calculate the coefficient of correlation between X and Y for the following.
X: 1 3 4 5 7 8 10
Y: 2 6 8 10 14 16 20
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