Скачать или смотреть ChebyShev's Inequality, Geometric Distribution | UPSC CSE Mains 2020 Statistics-1 1(c) Solution

In this video, we solve the *third part of the first problem* from **UPSC Civil Services Mains 2020, Statistics Optional (Paper I)**.

The problem involves a *geometric distribution* with probability function:
P(X = k) = (1/2)^k, where k = 1, 2, 3, …

We are asked to:
Use *Chebyshev’s inequality* to bound the probability P(|X - 2| ≤ 2).
Compare this bound with the **actual probability**.

Key steps covered in this video:
Derivation of the expectation and variance of the geometric distribution
Application of Chebyshev’s inequality
Exact calculation of P(|X - 2| ≤ 2)
Comparison of inequality bound (≥ 1/2) with the true probability (15/16)

*Final Results:*
Chebyshev’s bound: Probability ≥ 1/2
Exact probability: 15/16

This video is helpful for:
UPSC aspirants with *Statistics optional*
Students studying *probability theory*
Anyone learning *inequalities and distributions*

Highlights:
Clear explanation of Chebyshev’s inequality
Step-by-step derivations
Comparison between theoretical bounds and exact results


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