OP Malhotra **Theoretical Probability Distribution** ISC Class-12 Maths Solutions Ch-20. Step by step Solutions of OP Malhotra SK Gupta, Anubhuti Gangal S.Chand ISC Class-12 Mathematics with Exe-20(a), Exe-20(b), Exe-20(c), Exe-20(d), and Self Revision Questions. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

## OP Malhotra Theoretical Probability Distribution ISC Class-12 Maths Solutions Ch-20

Class: | 12th |

Subject: | Mathematics |

Chapter : | Ch-20 Theoretical Probability Distribution of Section -A |

Board | ISC |

Writer | OP Malhotra, SK Gupta, Anubhuti Gangal |

Publications | S.Chand Publications 2020-21 |

**-: Included Topics :- **

Exe-20(a),

Exe-20(b),

Exe-20(c),

Exe-20(d),

Self Revision

### OP Malhotra Theoretical Probability Distribution ISC Class-12 Maths Solutions Ch-20

**Probability Distribution Definition :-**

Probability distribution yields the possible outcomes for any random event. It is also defined based on the underlying sample space as a set of possible outcomes of any random experiment. These settings could be a set of real numbers or a set of vectors or set of any entities. It is a part of probability and statistics.

Random experiments are defined as the result of an experiment, whose outcome cannot be predicted. Suppose, if we toss a coin, we cannot predict, what outcome it will appear either it will come as Head or as Tail. The possible result of a random experiment is called an outcome. And the set of outcomes is called a sample point. With the help of these experiments or events, we can always create a probability pattern table in terms of variable and probabilities.

**Probability Distribution of Random Variables :-**

A random variable has a probability distribution, which defines the probability of its unknown values. Random variables can be discrete (not constant) or continuous or both. That means it takes any of a designated finite or countable list of values, provided with a probability mass function feature of the random variable’s probability distribution or can take any numerical value in an interval or set of intervals. Through a probability density function that is representative of the random variable’s probability distribution or it can be a combination of both discrete and continuous.

**Types of Probability Distribution :-**

There are two types of probability distribution which are used for different purposes and various types of the data generation process.

- Normal or Cumulative Probability Distribution
- Binomial or Discrete Probability Distribution

**Cumulative Probability Distribution :- **The cumulative probability distribution is also known as a continuous probability distribution. In this distribution, the set of possible outcomes can take on values on a continuous range.

**Normal Distribution :- **Since the normal distribution statistics estimates many natural events so well, it has evolved into a standard of recommendation for many probability queries.

**Discrete Probability Distribution :**– A distribution is called a discrete probability distribution, where the set of outcomes are discrete in nature.

**Binomial Distribution Examples :-**As we already know, binomial distribution gives the possibility of a different set of outcomes.

**Exe-20(a)**

### OP Malhotra Theoretical Probability Distribution ISC Class-12 Maths Solutions Ch-20

**Exe-20(b)**

OP Malhotra Theoretical Probability Distribution ISC Class-12 Maths Solutions Ch-20

**Exe-20(c)**

### OP Malhotra Theoretical Probability Distribution ISC Class-12 Maths Solutions Ch-20

**Negative Binomial Distribution :-**

In probability theory and statistics, if in a discrete probability distribution, the number of successes in a series of independent and identically disseminated Bernoulli trials before a particularised number of failures happens, then it is termed as the negative binomial distribution. Here the number of failures is denoted by ‘r’. For instance, if we throw a dice and determine the occurrence of 1 as a failure and all non-1’s as successes. Now, if we throw a dice frequently until 1 appears the third time, i.e.r = three failures, then the probability distribution of the number of non-1s that arrived would be the negative binomial distribution.

**Probability Distribution Function :-**

A function which is used to define the distribution of a probability is called a Probability distribution function. Depending upon the types, we can define these functions. Also, these functions are used in terms of probability density functions for any given random variable.

**Exe-20(d)**

OP Malhotra Theoretical Probability Distribution ISC Class-12 Maths Solutions Ch-20

Self Revision

### OP Malhotra Theoretical Probability Distribution ISC Class-12 Maths Solutions Ch-20

**-: End of Theoretical Probability Distribution ****S. Chand ISC Class-12 Maths Solution :-**

Return to :- OP Malhotra S. Chand ISC Class-12 Maths Solutions

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