Questions
2 questions per paper
Difficulty
Medium
Importance
High yield for HPCL/NTPC/ONGC
Overview
Probability is a cornerstone of quantitative aptitude and engineering mathematics in PSU exams, focusing on quantifying uncertainty in random processes. Mastering this topic allows you to predict outcomes and model system reliability, which is essential for solving technical MCQs efficiently.
Conditional Probability and Bayes Theorem
These concepts measure the likelihood of an event occurring given that another event has already occurred. Bayes Theorem is specifically used to update the probability of a hypothesis based on new evidence.
- P(A|B) = P(A intersection B) / P(B)
- P(A intersection B) = P(A) * P(B|A)
- Bayes Theorem: P(Ai|E) = [P(E|Ai)P(Ai)] / [sum of P(E|Aj)P(Aj)]
- Independent events: P(A intersection B) = P(A) * P(B)
Random Variables and Distributions
Random variables map outcomes of a random process to numerical values, categorized as discrete or continuous. Distributions describe how these values are spread, providing a framework for statistical inference.
- Binomial: P(X=r) = nCr * p^r * q^(n-r)
- Poisson: P(X=k) = (e^-lambda * lambda^k) / k!
- Exponential: f(x) = lambda * e^(-lambda * x)
- Uniform distribution mean: (a+b)/2
- Normal distribution: Z = (X - mu) / sigma
Mean, Median, Mode and Variance
These descriptive statistics summarize the central tendency and dispersion of a data set or distribution. In PSU exams, you are often asked to calculate variance for discrete or continuous variables given a function.
- E(X) = sum(x * P(x)) for discrete
- Var(X) = E(X^2) - [E(X)]^2
- Standard Deviation = sqrt(Variance)
- For normal distribution: Mean = Median = Mode
Formula Sheet
P(A U B) = P(A) + P(B) - P(A intersection B)
Binomial Mean = np, Variance = npq
Poisson Mean = Variance = lambda
Normal Distribution: f(x) = (1 / (sigma * sqrt(2*pi))) * e^(-(x-mu)^2 / (2*sigma^2))
Exam Tip
Always verify if the total probability sums to 1 before proceeding with mean or variance calculations.
Common Mistakes
- Confusing independent events with mutually exclusive events.
- Forgetting to normalize the probability density function (total area = 1) when finding a constant.
- Applying the Binomial formula when trials are not independent or probability changes.
More Revision Notes
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