Questions
~2 questions per paper
Difficulty
Medium
Importance
Medium yield for ONGC/NTPC/BHEL
Overview
Probability and Statistics is a fundamental quantitative pillar in PSU exams, focusing on the predictability of random events and data analysis. Mastering these concepts allows aspirants to score quick marks by applying standard distribution models to engineering problem scenarios.
Random Variables and Measures of Central Tendency
A random variable maps outcomes of random experiments to numerical values, serving as the basis for calculating average behavior. Mean, median, and mode provide snapshot summaries of data distributions often tested in basic statistics questions.
- Mean (Expected Value) E[X] = Σx*P(x)
- Variance V(X) = E[X^2] - (E[X])^2
- Standard Deviation σ = sqrt(Variance)
- Relationship: Mean ≥ Median ≥ Mode for positively skewed data
Binomial and Poisson Distributions
These are the two primary discrete probability distributions encountered in PSU exams for counting success in fixed trials or occurrences in intervals. Recognizing whether to use 'n' and 'p' (Binomial) or 'lambda' (Poisson) is critical.
- Binomial Probability: P(X=k) = nCk * p^k * (1-p)^(n-k)
- Binomial Mean: E[X] = np
- Binomial Variance: V(X) = np(1-p)
- Poisson Probability: P(X=k) = (e^-λ * λ^k) / k!
- Poisson property: Mean = Variance = λ
Normal (Gaussian) Distribution
The Normal distribution is the bedrock of continuous probability, characterized by its symmetric bell curve. PSU exams frequently test the empirical rule and Z-score transformations to determine probabilities under the curve.
- Normal PDF: f(x) = (1/σ*sqrt(2π)) * e^(-(x-μ)^2 / 2σ^2)
- Standard Normal Z-score: Z = (x - μ) / σ
- 68-95-99.7 Rule for μ±1σ, μ±2σ, and μ±3σ
- Area under the entire curve is always 1
Formula Sheet
E[X] = Σx*P(x)
V(X) = E[X^2] - (E[X])^2
Binomial: P(X=k) = nCk * p^k * q^(n-k)
Poisson: P(X=k) = (e^-λ * λ^k) / k!
Z = (x - μ) / σ
Exam Tip
Always verify if the distribution is discrete or continuous before selecting your formula, as selecting the wrong model is the most common cause of negative marking.
Common Mistakes
- Confusing Variance with Standard Deviation, leading to incorrect squaring errors.
- Using Binomial formula when the events are not independent or probability is not constant.
- Forgetting to check if the Poisson lambda value corresponds to the specific time interval given in the question.
More Revision Notes
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