60 C1813 Pages: 3

Module II

11 a) _ Define the following: (3)

i) Random experiment ii) Sample space 111) Event with examples
b) Two dice are tossed. Find the probability of getting ‘an even number on the first die (3) or a total of

8’.

OR

12 a) State and prove the addition rule of probability. (3) b) A box contains 6 red, 4 white and 5 black
balls. A person draws 4 balls from the box (3) at random. Find the probability that among the balls
drawn there is at least one ball of each colour.

Module 111
13 a) Find the value of ‘k’ for the following probability distribution. Also find its mean and
(3) variance.
xX 0 1 2 3
P(X=x) K/2 K/3 (പ) (2k-1)/6
b) Show that Poisson distribution is a limiting case of Binomial distribution. (3) OR

14 8) 8 binomial distribution consisting of 6 independent trials, probabilities of 1 and 2 (3) successes
are 0.28336 and 0.0506 respectively. Find its:

i) Probability distribution ii) Mean 111) Variance
b) Derive the mean and variance of a geometric distribution. (3)
Module 1५

15 a) Buses arrive at a specified stop at 15 minutes intervals from 6 am. If a passenger (3) arrives at the
stop at a random time that is uniformly distributed between 6.00 am and 6.30 am, find the
probability that he waits:

i) Less than 5 minutes forabus 14) At least 10 minutes for a bus

b) The weekly wages of 200 workmen are normally distributed about a mean of Rs. 500 (3) with a SD
of Rs 50. Estimate the number of workers whose weekly wages will be: i) Between Rs.400
and Rs. 600 11) Less than Rs. 400 111) Greater than Rs. 600

OR

16 The joint probability density function of 2 continuous random variables X and Y is given (6) by

f(x,y)=kxy, 0
i)k ii) P(X>3,y<4) 11) P(1P(x+y<3) v) Are X and Y independent.
Module V

17 a) Arandom sample of size 12 is taken from a normal population with SD 3. Find the (3) probability
that the variance of the sample lies between 3.4 and 14.8.

b) A random sample of size 15 from a normal population with mean 12 is found to have (3) variance 82
=5. Find the probability that the mean of the sample is less than 10.

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