Statistics 6401: Homework 1

• Read Preface
• Read Ch. 1
• Problems Ch1:  8, 9, 45, 72, 73, 74, 78, 79
• Read the Birthday Problem Stats Magazine paper. Birthday.pdf
• Do the following R Exercises.

• Exercise 1: Use R to

a) plot the Bin(n = 10, p = 0.5)

b) plot the Poi(lambda = 5)

c) Determine the 25th percentile for each distribution.

• Exercise 2: Write an R program that simulates a system of n components connected in parallel.  Let the probability that a component fails be p (use p = 0.01). Estimate the probability that the system fails. 

• Exercise 3: Using R simulate n = 100 standard normal values, square each value, and plot.  Comment on the shape of the distribution.

• Exercise 4 :

a) Using R plot the exponential p.d.f. for lambda = 0.4, 1, 8  Determine the 25th percentile for each distribution.

b) Using R plot the gamma p.d.f. for alpha = 1, lambda = 0.4, 1, 8 and for alpha = 0.5, 1, 5, lambda = 2.5  Determine the 25th percentile for each distribution.