# Familiarization with R and Probability Functions

Autor: Anthony Owusu • May 25, 2019 • Research Paper • 442 Words (2 Pages) • 137 Views

**Page 1 of 2**

Student Name: Anthony Owusu

Engineering 202

Assignment 1

Familiarization with R and Probability Functions

Due April 4, 2016

Instructions: the purpose of these problems is to get you familiar with the references and the R help facility. These exercises will use two distribution, Normal (Gaussian) and Poisson in both the density and cumulative forms (dnorm, pnorm, dpois, and ppois), the R commands curve, hist, and the operation for creating and filling a simple one-dimensional data vector. Insert both the commands you used and the plots you created to answer these questions.

You can learn how to perform problems 1 and 2 by reading and repeating the commands in the Ricci paper on pages 8 and 9 and problems 3 and 4 by consulting the Chi Yau R tutorial (see the probability distribution reference, 1b)

- Using the “curve” command, create

- the normal distribution probability density function with mean 10 and standard distribution density function. Show the command and the screen plot output

Command: curve(dnorm (x,10))

Plot Output: [pic 1]

- the cumulative normal distribution function

Command: curve (pnorm (x))

Plot: [pic 2]

- the probability density function for the T-distirbution probability density function using a non-centrality parameter (ncp) of 5 for the following degrees of freedom: 1, 5, 25. What is happening to the distribution?

Commands: curve (dt (x, 1, 5, log=FALSE)), curve (dt (x, 5, 5, log=FALSE)), curve (dt (x, 25, 5, log=FALSE))

Outputs: [pic 3] [pic 4] [pic 5]

As the number of degree of freedoms increases, t-distribution approaches a normal distribution.

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