Page 156 - DMTH404_STATISTICS

Statistics

Notes  When two or more random variables X and Y are studied simultaneously on a sample
space, we get a joint probability distribution. Consider the experiment of throwing two
unbiased dice. If X denotes the number on the first and Y denotes the number on the
second die, then X and Y are random variables having a joint probability distribution.
When the number of random variables is two, it is called a bi-variate probability
distribution and if the number of random variables become more than two, the distribution
is termed as a multivariate probability distribution.
10.7 Keywords

Expected value: Expected value of a constant is the constant itself, i.e., E(b) = b, where b is a
constant.

Variance: The variance of a constant is zero.
10.8 Self Assessment

1. When a random variable is expressed in monetary units, its expected value is often termed
as expected monetary value and symbolised by .....................

(a) probability distribution (b) EMV
(c) Covariance (d) random variables
2. The set of all possible values of the random variable X along with their respective marginal
probabilities is termed as the marginal .................... of X.
(a) probability distribution (b) EMV
(c) Covariance (d) random variables
3. If X and Y are two .................... , then E(X + Y) = E(X) + E(Y).

(a) probability distribution (b) EMV
(c) Covariance (d) random variables
4. The mean of the product of deviations of values from their respective means, is known as
the .................... of X and Y denoted as Cov(X, Y) or  XY .
(a) probability distribution (b) EMV
(c) Covariance (d) random variables

10.9 Review Questions

1. ABC company estimates the net profit on a new product, that it is launching, to be Rs
30,00,000 if it is successful, Rs 10,00,000 if it is moderately successful and a loss of Rs
10,00,000 if it is unsuccessful. The firm assigns the following probabilities to the different
possibilities : Successful 0.15, moderately successful 0.25 and unsuccessful 0.60. Find the
expected value and variance of the net profits.

Hint : See example 5.
2. There are 4 different choices available to a customer who wants to buy a transistor set. The
first type costs Rs 800, the second type Rs 680, the third type Rs 880 and the fourth type Rs
1 1 1 1
760. The probabilities that the customer will buy these types are , , and respectively.
3 6 4 4

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