SSC online notified the detailed syllabus for paper III. There are SSC 2020 **online tests** available which help candidates to boost their score through regular practice.

**Random Variable and Probability Distributions**

- Here the outcome is observed by studying the nature of a random variable over a random experiment.
- It is a statistical term using the concept of probability.
- There are two types of random variables: Discrete and Continuous.
- The probability distribution of a random variable is defined as the probability of different values observed for a random variable.
- The Probability distribution function can be expressed as f(x), where x is the random variable.
- Probability distribution of a random variable can be of two types: Normal and Binomial

**Example:** If we toss a coin then the probability of getting head is 1/2.

**Explanation: **Here tossing of a coin is a random experiment and the probability of getting head or tail is half at each random experiment.

__Sampling Theory__

- Sampling is a statistical process where the study takes place on a large number of data sets.
- Here data is collected from a small group of population out of a large set of the population to estimate the characteristics of the whole population.
- It is an economical process where data size is large.
- It also uses the concept of probability.
- Finding out the sample size and sample parameter are the two basic but important parts of the sampling theory.

__Process Of sampling:__

- Identify the population.
- Create a sample set from the population.
- Define the sample set.
- The sample set of population must reflect all the attributes or characteristics of the whole population.
- Identify the errors.
- Analyze the result.

__Types of sampling:__

- Random Sampling
- Systematic sampling
- Stratified sampling
- Cluster sampling
- Merit Sampling

**Example:** Let’s find out the two monitor of the class which can represent the whole class.

**Explanation: **

Here the whole class is divided into two sets boys and girls.

Out of boys set we can select a boy as monitor either random or through election or on the basis of merit.

Same as above we can select a girl as a monitor from the girls set.

Announce the boy and girl as monitor of the class.

__Statistical Inference__

- is altered randomly. This used the concept of random sampling in decision making.
- It takes uncertainty into account while drawing the conclusion.

__Process of Statistical Inference:__

- Put up a theory.
- Have a research on your theory and create a hypothesis.
- Apply the variables on your hypothesis
- Identify the application
- Form an anti-thesis
- Collect the data
- Apply the test on the basis of data to disapprove anti-thesis.

**Example:** A dice has been thrown for 10 times and following observations were recorded:

One: 2

Two: 1

Three: 2

Four: 1

Five: 1

Six: 3

Then find the probability of getting 6, if the dice have been randomly thrown?

**Answer: **Probability of getting 6 on dice** **

** =** Number of times 6 appeared in observation Total Number of Observation** **

= 310

= **0.3**

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