Read sections 3.1 to 3.3 of the S manual and use this to do the following exercises. Include answers to all questions in your lab report.

1. Create a vector p containing nineteen equally-spaced values between 0 and 1. Do not use the values of 0 or 1 themselves (i.e., start at .05 and end at .95).

2. Find the pth quantile of the exponential distribution with scale parameter for each of the values in p. Save these values in a vector yp. Note that you can use a single command in S applied to the vector p which will operate on each entry of p and create a vector of the same length, rather than finding each pth quantile separately.

3. Compute the density of the exponential distribution (note : rate in the command, is the inverse of the scale parameter) with scale parameter for each of the values in yp using the S function dexp. Save these values in a vector fy.

4. Evaluate the distribution function using each of the values in the vector yp. Save your answers in a vector Fy.

5. Make a scatter plot of fy versus yp. These points are from what curve? (Remember to open grahpical window).

6. Compare your vectors p and Fy. They should be the same. Why?