Book back answers and solution for Exercise questions - Discrete random variable, Continuous random variable - Exercise Problem Questions with Answer, Solution

**Exercise 6.1**

1. Construct cumulative distribution function for
the given probability distribution.

2. Let X be a discrete random variable
with the following p.m.f

Find and plot the c.d.f. of X .

3. The discrete random variable X has
the following probability function

where k is a constant. Show that k = 1/81

4. The discrete random variable X has
the probability function

Show that k = 0 ⋅ 1 .

5. Two coins are tossed simultaneously.
Getting a head is termed as success. Find the probability distribution of the
number of successes.

6. A continuous random variable X has
the following probability function

(i) Find k

(ii) Ealuate p( x < 6), p(x ≥ 6) and
p(0 < x < 5)

(iii) If P(X ≤ x) > 1/2 , then find
the minimum value of x .

7. The distribution of a continuous
random variable X in range (–3, 3) is given by p.d.f.

Verify that the area under the curve is
unity.

8. A continuous random variable X has
the following distribution function:

Find (i) k and (ii) the probability
density function.

9. The length of time (in minutes) that
a certain person speaks on the telephone is found to be random phenomenon, with
a probability function specified by the probability density function f (x) as

(a) Find the value of A that makes f (x)
a p.d.f.

(b) What is the probability that the
number of minutes that person will talk over the phone is (i) more than 10
minutes, (ii) less than 5 minutes and (iii) between 5 and 10 minutes.

10. Suppose that the time in minutes
that a person has to wait at a certain station for a train is found to be a
random phenomenon with a probability function specified by the distribution
function

(a) Is the distribution function
continuous? If so, give its probability density function?

(b) What is the probability that a
person will have to wait (i) more than 3 minutes, (ii) less than 3 minutes and
(iii) between 1 and 3 minutes?

11. Define random variable.

12. Explain what are the types of random
variable?

13. Define discrete random variable.

14. What do you understand by continuous
random variable?

15. Describe what is meant by a random
variable.

16. Distinguish between discrete and
continuous random variable.

17. Explain the distribution function of
a random variable.

18. Explain the terms (i) probability
mass function, (ii) probability density function and (iii) probability
distribution function.

19. What are the properties of (i)
discrete random variable and (ii) continuous random variable?

20. State the properties of distribution
function.

**Answers:**

Tags : Problem Questions with Answer, Solution , 12th Business Maths and Statistics : Chapter 6 : Random Variable and Mathematical Expectation

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12th Business Maths and Statistics : Chapter 6 : Random Variable and Mathematical Expectation : Exercise 6.1: Random variable | Problem Questions with Answer, Solution

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