Random Variables and Probability Distributions SSC CGL Tier 2 Paper 2

In SSC CGL Tier 2 SSC JSO (Junior Statistical Officer Paper II), questions on Random Variables and Probability Distributions are very important. These concepts help in modelling uncertainty, understanding data patterns, and predicting outcomes.This blog covers random variables, types of distributions, and joint distributions with easy examples and formulas.

1. Random Variable (RV)

Definition

A random variable is a numerical outcome of a random experiment.

• Types of Random Variables:
  1. Discrete Random Variable – takes countable values (e.g., number of heads in 3 coin tosses).
  2. Continuous Random Variable – takes uncountable values in an interval (e.g., height, weight).

Example:

• Toss a die → X = number on top face → Discrete
• Time to complete a task → Y = time in minutes → Continuous

2. Probability Distributions

3. Common Probability Distributions

4. Joint Probability Distributions

Definition

5. Key Formulas:

Below are the key formulas:

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Key Takeaways for SSC CGL Tier 2

• Random Variable → numeric outcome of experiment.
• Discrete vs Continuous → countable vs uncountable values.
• Binomial & Poisson → discrete distributions.
• Normal & Exponential → continuous distributions.
• Joint distribution → probability of two RVs together.
• Practice marginal and conditional distributions for exam speed.

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