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The CLT states that, for large n, the distribution of the sample mean approaches a Normal distribution. Mathematically, Xn X₂ →º N (µ‚, 2/² ). D n where →D means 'converges in distribution'; it's implied here that this convergence takes place as n, or the number of underlying random variables, grows. This is an extremely powerful result, because it holds no matter what the distribution of the underlying random variables is. Task Using software R, demonstrate that CLT holds on the example of the Exponential Distribution. Use λ = 5 for de-ix ,x ≥ 0.

The CLT states that, for large n, the distribution of the sample mean approaches a Normal distribution. Mathematically, Xn X₂ →º N (µ‚, 2/² ). D n where →D means 'converges in distribution'; it's implied here that this convergence takes place as n, or the number of underlying random variables, grows. This is an extremely powerful result, because it holds no matter what the distribution of the underlying random variables is. Task Using software R, demonstrate that CLT holds on the example of the Exponential Distribution. Use λ = 5 for de-ix ,x ≥ 0.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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could you produce 3 histogram ggplots for this question, similar to the ones i uploaded using R

  1. Plot the Histogram for the Exponential distribution
  2. Plot the Histogram for the Normal distribution
  3. plot for comparison between exponential and normal,

with a key and also could you outline the graphs with a normal curve and provide an explanation for th eobservations and what the graph tells us .

04 I Demonstrating Central Limit Theorem 1. Value The Distribution of Sample Means and the Uniform Distribution 04 Distribution of Means Uno Distribution 00 ampla ass trearotidal variazas 14 0.001611049547 [1] "The hmber of similations in 2008 # [1] "The difference between sample and theoretical means is 0.00151247649783848" # [1] "The difference between sample and theoretical variances is 0.0012342020050992" Demonstrating Central Limit Theorem Uniform Distribution 1500- Value Value Type Hulh Normal Dibution The Distribution of Sample Means and the Uniform Distribution Value Type [1] "The Number of simulations is 10000" [1] "the difference between sample and theoretical means is 0.000366877283006026" # [1] "The difference between sample and theoretical variances is 0.008186210166330476 Demonstrating Central Limit Theorem of Sample Man bution of Sample Man Nouton Value The Distribution of Sample Means and the Uniform Distribution Distribution of Means Uniform Distribution Otribution of Sample Mean Normal Dibution
Transcribed Image Text:04 I Demonstrating Central Limit Theorem 1. Value The Distribution of Sample Means and the Uniform Distribution 04 Distribution of Means Uno Distribution 00 ampla ass trearotidal variazas 14 0.001611049547 [1] "The hmber of similations in 2008 # [1] "The difference between sample and theoretical means is 0.00151247649783848" # [1] "The difference between sample and theoretical variances is 0.0012342020050992" Demonstrating Central Limit Theorem Uniform Distribution 1500- Value Value Type Hulh Normal Dibution The Distribution of Sample Means and the Uniform Distribution Value Type [1] "The Number of simulations is 10000" [1] "the difference between sample and theoretical means is 0.000366877283006026" # [1] "The difference between sample and theoretical variances is 0.008186210166330476 Demonstrating Central Limit Theorem of Sample Man bution of Sample Man Nouton Value The Distribution of Sample Means and the Uniform Distribution Distribution of Means Uniform Distribution Otribution of Sample Mean Normal Dibution
The CLT states that, for large n, the distribution of the sample mean approaches a Normal distribution. Mathematically, X₁ +" N (1, 0-²) 9 n Xn where → →D means 'converges in distribution'; it's implied here that this convergence takes place as ʼn, or the number of underlying random variables, grows. This is an extremely powerful result, because it holds no matter what the distribution of the underlying random variables is. Task Using software R, demonstrate that CLT holds on the example the Exponential Distribution. Use λ = 5 for de-2x, x ≥ 0.
Transcribed Image Text:The CLT states that, for large n, the distribution of the sample mean approaches a Normal distribution. Mathematically, X₁ +" N (1, 0-²) 9 n Xn where → →D means 'converges in distribution'; it's implied here that this convergence takes place as ʼn, or the number of underlying random variables, grows. This is an extremely powerful result, because it holds no matter what the distribution of the underlying random variables is. Task Using software R, demonstrate that CLT holds on the example the Exponential Distribution. Use λ = 5 for de-2x, x ≥ 0.
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