Questions
~2 questions per paper
Difficulty
Medium
Importance
Medium yield for HPCL/NTPC/ONGC
Overview
Probability and Statistics deal with the analysis of random phenomena and data interpretation. In PSU exams, this topic is critical for reliability analysis and quality control, requiring a solid grasp of distribution properties and central tendency metrics.
Random Variables and Probability Measures
A random variable maps outcomes of a random process to numerical values. Mastering the distinction between discrete and continuous variables is essential for selecting the correct probability mass or density function.
- P(A|B) = P(A intersection B) / P(B)
- Sum of all probabilities in a distribution equals 1
- E[X] = summation(x*P(x)) for discrete variables
- Independent events: P(A intersection B) = P(A)*P(B)
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Standard Probability Distributions
Discrete distributions like Binomial and Poisson model counting processes, while the Normal distribution handles continuous data. These are frequently used to solve PSU-level questions involving production failure rates and error analysis.
- Binomial: P(X=r) = nCr * p^r * q^(n-r)
- Poisson: P(X=k) = (lambda^k * e^-lambda) / k!
- Normal distribution follows the bell curve shape
- Mean of Binomial distribution = np
Measures of Central Tendency and Dispersion
These metrics describe the behavior of a dataset. Understanding mean, median, mode, and variance is vital for interpreting raw data sets provided in technical exam questions.
- Mean = (sum of values) / N
- Variance = E[X^2] - (E[X])^2
- Standard Deviation = square root of Variance
- Mode is the most frequently occurring value
Formula Sheet
P(A|B) = P(A cap B) / P(B)
E[X] = sum(x * P(x))
Var(X) = E[X^2] - (E[X])^2
P(X=k) = (lambda^k * exp(-lambda)) / k!
Exam Tip
Always verify if the given events are independent or dependent before applying multiplication rules, as this is the most common trap in conditional probability questions.
Common Mistakes
- Confusing the Binomial distribution (fixed trials) with Poisson (rate-based events)
- Forgetting to subtract the square of the mean when calculating variance
- Misinterpreting 'at least' or 'at most' conditions leading to incorrect summation ranges
More Revision Notes
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