Solved Examples on Discrete Probability Distribution

Types of Discrete Probability Distribution

Practice Questions on Discrete Probability Distribution

Example 1: Construct the discrete probability table when a coin is tossed two times and X be random variable representing the number of one head.

Solution:

Sample space of two coin tossed = 4 i.e., {HH, HT, TH, TT}

X: Number of one head

The below table represents the discrete probability.

X	{HT}	{TH}
P (X = x)	1 / 4	1/4

Example 2: Find the value of p from the given discrete probability table.

X	3	4	5	6
P (X = x)	0.1	p	0.2	0.4

Solution:

To find the value of p we will use the discrete probability condition.

∑ P (X =x) = 1

0.1 + p + 0.2 + 0.4 = 1

0.7 + p = 1

p = 1 – 0.7

p = 0.3

Example 3: Find the mean of discrete probability distribution using below table.

X	2	3	4	5
P (X = x)	0.16	0.45	0.32	0.07

Solution:

To find the mean of discrete probability distribution we use formula:

E[X] = ∑ [ x P(X =x)]

E[X] = 2 × 0.16 + 3 × 0.45 + 4 × 0.32 + 5 × 0.07

E[X] = 0.32 + 1.35 + 1.28 + 0.35

E[X] = 3.3

Example 4: If there are 15 pens in which 3 pens are defective and the probability of pen is defective 0.5 then, find the discrete probability of pen to be defective.

Solution:

To find the required probability we use Binomial Distribution

P (X = x) = ⁿC_x p^x (1-p) ^n-x

P (X = 3) = ¹⁵C₃ p³ (1-p) ^15-3

P (X = 3) = ¹⁵C₃ (0.5)³ (1 – 0.5) ¹²

P (X = 3) = 455 × (0.5)³ × (0.5) ¹²

P (X = 3) = 455 × (0.5)¹⁵

P (X = 3) = 0.014

Discrete Probability Distribution

Discrete probability distribution counts occurrences with finite outcomes. The common examples of discrete probability distribution include Bernoulli, Binomial and Poisson distributions.

In this article we will explore discrete probability distribution along with discrete probability distribution definition, discrete probability distribution condition and discrete probability distribution formulas.

Table of Content

What is Discrete Probability Distribution?

Conditions for Discrete Probability Distribution

Discrete Probability Distribution Formulas
Discrete Probability Distribution Mean
Discrete Probability Distribution Variance
How to Find Discrete Probability Function
Types of Discrete Probability Distribution

Solved Examples on Discrete Probability Distribution

Discrete Probability Distribution

Similar Reads

Contact Us