Familiarization with R and Probability Functions

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)

1. Using the “curve” command, create

1. 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]

1. the cumulative normal distribution function

Command: curve (pnorm (x))

Plot: [pic 2]

1. 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.