Let X = = Σ" X;. X₁. j=1 0 Explain why X converges in probability to 0+1*

MATLAB: An Introduction with Applications
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Chapter1: Starting With Matlab
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Let \(\overline{X} = \frac{1}{n} \sum_{j=1}^{n} X_j\).

Explain why \(\overline{X}\) converges in probability to \(\frac{\theta}{\theta + 1}\).
Transcribed Image Text:Let \(\overline{X} = \frac{1}{n} \sum_{j=1}^{n} X_j\). Explain why \(\overline{X}\) converges in probability to \(\frac{\theta}{\theta + 1}\).
**Text Transcription for Educational Website:**

Let \( X_1, X_2, \ldots, X_n \) be a random sample from a population with cumulative distribution function

\[ F(x) = x^\theta, \quad 0 < x < 1. \]

You may assume the unknown parameter \(\theta > 0\).
Transcribed Image Text:**Text Transcription for Educational Website:** Let \( X_1, X_2, \ldots, X_n \) be a random sample from a population with cumulative distribution function \[ F(x) = x^\theta, \quad 0 < x < 1. \] You may assume the unknown parameter \(\theta > 0\).
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