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Statistics

Notes Discrete Probability Distribution: The distribution of a discrete random variable is called the
Discrete Probability Distribution.
Continuous Probability Distribution: The distribution of a continuous random variable is called
a Continuous Probability Distribution and the corresponding probability function p(X) is termed
as the Probability Density Function.

4.5 Self Assessment

State whether the following statements are true or false:
(a) A random variable takes a value corresponding to every element of the sample space.
(b) The probability of a given value of the discrete random variable is obtained by its
probability density function.
(c) Distribution function is another name of cumulative probability function.
(d) Any function of a random variable is also a random variable.

4.6 Review Questions

1. An urn contains 4 white and 3 black balls. 3 balls are drawn at random. Write down the
probability distribution of the number of white balls. Find mean and variance of the
distribution.

2. A consignment is offered to two firms A and B for Rs 50,000. The following table shows the
probability at which the firm will be able to sell it at different prices :

SellingPrice in Rs) 40,000 45,000 55,000 70,000
(

Prob of A 0.3 0.4 0.2 0.1

.

.
Prob of B . 0 1 . 0 2 . 0 4 03

Which of the two firms will be more inclined towards the offer?
3. If the probability that the value of a certain stock will remain same is 0.46, the probabilities
that its value will increase by Re. 0.50 or Re. 1.00 per share are respectively 0.17 and 0.23
and the probability that its value will decrease by Re. 0.25 per share is 0.14, what is the
expected gain per share?
4. In a college fete a stall is run where on buying a ticket a person is allowed one throw of
two dice. If this gives a double six, 10 times the ticket money is refunded and in other cases
nothing is refunded. Will it be profitable to run such a stall? What is the expectation of the
player? State clearly the assumptions if any, for your answer.
5. The proprietor of a food stall has introduced a new item of food. The cost of making it is
Rs 4 per piece and because of its novelty, it would be sold for Rs 8 per piece. It is, however,
perishable and pieces remaining unsold at the end of the day are a dead loss. He expects
the daily demand to be variable and has drawn up the following probability distribution
expressing his estimates:
No. of pieces demanded : 50 51 52 53 54 55
Probability : 0.05 0.07 0.20 0.35 0.25 0.08
Compute his expected profit or loss if he prepares 53 pieces on a particular day.

Answers: Self Assessment

1. T 2. F 3. T 4. T

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