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BCA-203N · Numerical Analysis and Statistical Techniques
Unit 5

Random Variables & Theoretical Probability Distributions

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Unit 5 Learning Hub

Random Variables & Theoretical Probability Distributions

Official MJPRU BCA Unit 5: Random Variables & Theoretical Probability Distributions for BCA-203N (Numerical Analysis and Statistical Techniques).

Syllabus Topics:Random Variables: Definition, Sample Space Mapping, Discrete vs Continuous Random VariablesProbability Mass Function (PMF): Definition, Properties (P(X=x) >= 0, sum P(x) = 1), Cumulative Distribution Function (CDF)Probability Density Function (PDF): Definition, Properties (f(x) >= 0, integral f(x)dx = 1), Cumulative Distribution FunctionMathematical Expectation (Expected Value): E(X) Formula for Discrete and Continuous Distributions, Properties of ExpectationVariance and Standard Deviation: Var(X) = E(X^2) - [E(X)]^2, Properties of Variance, Moments of DistributionsDiscrete Uniform Distribution: PMF, Mean, Variance, Real-World Applications (Fair Die Toss)Bernoulli Distribution: Single Trial with Success Probability p, Mean = p, Variance = pqBinomial Distribution: Assumptions (n Independent Bernoulli Trials), PMF P(X=r) = nCr * p^r * q^(n-r)Characteristics of Binomial Distribution: Mean = np, Variance = npq, Conditions (Mean > Variance), Practical ApplicationsPoisson Distribution: Rare Events Model, Limiting Form of Binomial Distribution (n -> inf, p -> 0, np = lambda)Characteristics of Poisson Distribution: PMF P(X=r) = (e^(-lambda) * lambda^r) / r!, Mean = Variance = lambdaContinuous Uniform (Rectangular) Distribution: PDF, CDF, Mean = (a+b)/2, Variance = (b-a)^2 / 12Exponential Distribution: Memoryless Property, PDF f(x) = lambda * e^(-lambda*x), Mean = 1/lambda, Reliability ModelsNormal (Gaussian) Distribution: Bell-Shaped Curve, PDF Formula, Parameters Mean (mu) and Variance (sigma^2)Properties of Normal Curve: Symmetry about Mean, Unimodal, Area Properties (Empirical Rule 68-95-99.7%)Standard Normal Distribution (Z): Z-Score Transformation Z = (X - mu)/sigma, Standard Normal Probability Tables
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Introduction to Computers & The IPO Cycle

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Topic 1 · The foundation of modern computing

Introduction to Computers & The IPO Cycle

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Ready to master this concept? Give it a quick read & tap the check!

💡 The Big Picture:A computer is an electronic system that takes raw data as Input, processes it under programmed logic, and produces meaningful Information as Output.
🍪 Everyday Analogy:Think of baking cookies: Flour & Sugar (Input) ➔ The Oven (Processing) ➔ Warm Delicious Cookie (Output)! 🍪
Key Exam Takeaways
  • ·Data = Raw, unprocessed facts without context (e.g. 42, 'apple').
  • ·Information = Structured data with meaning (e.g. 'Temperature: 42°C').
  • ·Hardware is what you can touch; Software is the instructions running inside.
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Which of the following represents unprocessed raw facts?

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