Project Assignment

Benefits:

• Very straightforward authoring syntax (Markdown)
• Easy incorporation of R code and it's output (including plots)
• Support for LaTeX equations using MathJax
• Many options for slide transitions and slide navigation
• Ability to customize the appearance of slides using CSS
• Extensive support for authoring and previewing presentations within the RStudio IDE
• Can be easily published as either a standalone HTML file or to RPubs

Presentation Proposal

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This project aims to demonstrate the ability to run embedded R code,through the investigation of an exponential distribution in R comparing it with the Central Limit Theorem. The exponential distribution was simulated in R with rexp(n, lambda) where lambda is the rate parameter.

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The mean of exponential distribution is 1/lambda and the standard deviation is also 1/lambda. lambda was set = 0.2 for all of the simulations. It will be investigated the distribution of averages of 40 exponentials.

Expo_Distr <- NULL
lambda<- 0.2
z<- 40
d<- 1000
for ( i in 1:d) 
Expo_Distr <- c(Expo_Distr, mean(rexp(z,lambda)))
theorectical_mean<- mean(rexp(d,lambda))
sample_mean<- mean(Expo_Distr)
theorectical_variance <- var(rexp(d,lambda))
sample_variance<- var(Expo_Distr)
print(theorectical_mean)

[1] 5.200037

print(sample_mean)

[1] 4.972113

print(theorectical_variance)

[1] 27.74256

print(sample_variance)

[1] 0.6482529

The exponential distribution was built with 1000 values and lambda = 0.2, its mean and variance are approximately 1/lambda and 1/(lambda²⁾ respectively ( ~ 5 and ~ 25). At the same time the distribution utilizing the mean of the samples from the exponential distribution is normal, which mean is also ( ~ 5 ) and its variance has a proportionality with the population variance which is inversely proportional to the sample size, for this case the variance is (1/(lambda^2))/(size of samples) which represents 25/40 ~ 0.6