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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