Questions
2 questions in major PSU papers
Difficulty
Medium
Importance
Moderate yield for HPCL/ONGC/BHEL
Overview
Probability and Statistics is a fundamental quantitative module that tests your ability to model uncertainty and interpret data sets. In PSU exams, this topic is highly scoring if you master the underlying properties of distribution functions and central tendency measures, as questions are often direct applications of standard formulas.
Central Tendency and Dispersion
These measures represent the center and spread of data sets, which are critical for processing raw engineering data. You must be comfortable calculating mean, median, and mode for both discrete and continuous grouped data.
- Mean: (Σfx)/Σf
- Median: Midpoint of ordered data (n/2 position)
- Mode: Value with highest frequency
- Variance: σ² = Σ(xi - μ)²/n
- Standard Deviation: √Variance
Probability Distributions
Distributions categorize the behavior of random variables under specific conditions. Understanding the selection criteria between Binomial, Poisson, and Normal distributions is the key to solving numerical problems efficiently.
- Binomial: P(X=k) = nCk * p^k * q^(n-k)
- Poisson: P(X=k) = (e^-λ * λ^k) / k!
- Normal: Z = (x - μ) / σ
- Binomial mean: np, variance: npq
- Poisson mean = variance = λ
Correlation and Regression
These concepts quantify the strength and direction of relationships between two variables. Expect numerical problems where you are asked to compute correlation coefficients or linear regression slope constants.
- Pearson Correlation Coefficient (r) range: [-1, 1]
- Regression line of Y on X: Y - meanY = b(X - meanX)
- r = Cov(X,Y) / (σx * σy)
- If r = 0, variables are uncorrelated
- If r = 1, perfect positive correlation
Formula Sheet
Mean: x̄ = Σxi/n
Variance: σ² = E[X²] - (E[X])²
Binomial Prob: P(X=k) = nCk * p^k * q^(n-k)
Poisson Prob: P(X=k) = (e^-λ * λ^k) / k!
Correlation: r = Σ((x-x̄)(y-ȳ)) / sqrt(Σ(x-x̄)² * Σ(y-ȳ)²)
Exam Tip
Always verify if a probability distribution problem provides n and p (Binomial) or just the mean λ (Poisson) before choosing your formula to save time.
Common Mistakes
- Confusing Variance (σ²) with Standard Deviation (σ) in the final answer
- Failing to convert the 'n' or 'p' values correctly for Poisson approximations in Binomial distributions
- Ignoring the condition of 'mean = variance' when identifying Poisson distribution problems
More Revision Notes
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