Probability and Statistics Topics - GATE ME Syllabus

1

Definitions of probability

Classical, empirical, axiomatic definitions.

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📌 Key FormulaP(A) = n(A)/n(S)

2

Sampling theorems

Central limit and other sampling distributions.

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📌 Key FormulaSample mean distribution

3

Conditional probability

Probability of event given another has occurred.

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📌 Key FormulaP(A|B) = P(A∩B)/P(B)

4

Mean deviation

Average absolute deviation from mean.

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📌 Key FormulaMD = Σ |x - mean|/n

5

Median deviation

Deviation from median.

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📌 Key FormulaFrom median

6

Mode deviation

Deviation from mode.

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📌 Key FormulaFrom mode

7

Standard deviation

Root mean square deviation.

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📌 Key Formulaσ = √(variance)

8

Random variables

Discrete and continuous random variables.

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📌 Key FormulaE[X], Var(X)

9

Binomial distributions

For fixed trials with success probability.

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📌 Key FormulaP(k) = C(n,k) p^k (1-p)^{n-k}

10

Poisson distributions

For rare events in interval.

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📌 Key FormulaP(k) = e^{-λ} λ^k / k!

11

Normal distributions

Bell-shaped continuous distribution.

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📌 Key FormulaZ = (x-μ)/σ