Word Count : 227

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Given,

x/y	1	2	3
1	0.2	0.2	0.1
2	0.1	0.3	0.1

a) To find the marginal distributions, we have to find the marginal totals, i.e. row totals and column totals as shown in the following table:

______ _________ ____ _________ __________ ____ __________ _________ _______ _______ _______.
_______ ___ _______ ______ _____ ____.
_________ _______ _____ ______ ___.
________ ________ _______ _____ ________ _____ _______ __________.
____ ________ _____ ______ ____ _______ _______.
_____ ______ ___ ____ ___ ______ __________ _______ _________.
____ _______ __________ _________ _______ _______ _______ ____ __________ ___ ______.
______ _________ ____ ____ _______ ___ ________ _____ ______ ________ ________.
________ ______ ____ _______ _______ ______ ________ ________ ___ _________.
___ ___ ___ _______ _______ ___ _________ _______.
___ _______ _________ ____ _______ _________ ________.
______ ________ ___ ______ _________ ______ ___ ________ _______ __________.
_____ ________ ________ _______ ______ ___ __________ _____ _____ _______.
________ ______ _____ ____ _______ ___ _________ _____ _______ ________ ______ ______.
____ ____ ____ ________ _______ _________ ___.
___ ____ ______ _______ ________.
_________ _____ ____ ___ _______ ___ ________ __________.
_____ ________ _____ _______ _______ _________ __________ ________.
_______ _________ ________ _______ __________ _____ _______ ___ ______ ______ _________ _______.
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Y X	1	2	3
1	0.2	0.2	0.1
2	0.1	0.3	0.1

Find
a) The marginal distributions.
b) The conditional distribution of Y given X = 2

An insurance company selected 6000 drivers from a city at random in order to find a relationship between age and accidents. The following table shows the results to these 6000 drivers.

Age of drivers (in years) Class Interval	Accidents in one year
	0	1	2	3	4 or more
18 – 25	700	310	225	110	85
25 – 40	1100	290	200	105	80
40 – 50	1200	235	175	80	55
50 and above	600	205	140	70	35

 If a driver from the city is selected at random, find the probability of the following events:
a) Age lying between 18 – 25 and meet 3 accidents
b) Age lying between 18 – 40 and meet 1 accident
c) Age more than 25 years and meet at most one accident
d) Having no accident in the year
e) Age lying between 18 – 40 and meet at least 3 accidents

If the probability that an individual suffers a bad reaction from an injection of a given  serum is 0.002, determine the probability that out of 400 individuals
(i) exactly 2
(ii) more than 3
(iii) at least one
 individuals suffer from bad reaction.

A die is rolled. If the outcome is a number greater than 2, what is the probability that it is an odd prime number?

A player tosses two unbiased coins. He wins Rs. 10 if 2 heads appear, Rs. 5 if one head appears and Rs 1 if no head appears. Find the expected value of the amount won by him.