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 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.
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.
- 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:
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
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