DESCRIPTION

Please keep in mind the OMSI rules.

Save your files often.

Submit each answer individually and make sure you receive the notification of successful submission.

Don't wait till the last moment to submit all answers, as there might be network traffic in the last 5 minutes causing unexpected delay and failure.  

Remember that clicking CopyQtoA will copy the entire question box to the answer box.

In questions involving code which will PARTIALLY be given to you in the question specs, you may need to add new lines. 
There may not be information given as to where the lines should be inserted. 

MAKE SURE TO RUN THE R CODE ANSWER IN PROBLEMS THAT INVOLVE R CODE!

QUESTION

(Text answer - 20 pts)  Consider the discussion at the top of p.209.  In
class, we stated that X_i will have the same distribution as the
population even in the case of simple random sampling.  We cited an
example from earlier in the book as being similar.  Which example was
that?

QUESTION

(Text answer - 20 pts) Consider Eqn. (7.124), specifically the expression
Sigma-inverse.  (NOT Sigma itself.)  What part of Eqn. (7.81), if any,
does Sigma-inverse roughly correspond to?


QUESTION


(Text answer - 20 pts) In which of the following pair(s) of distributions, 
one is a special case of the other?

[Select all that apply]

(i)   Exponential, Poisson
(ii)  Binomial, Normal
(iii) Poisson, Normal
(iv)  Bernoulli, Binomial 
(v)   Exponential, Gamma


QUESTION 

(Text answer - 20 pts)  A distribution for random variable X is said to have
an increasing failure rate if f_X(t) / [1 - F_X(t)] is increasing for t
in the support of X, with similar definitions for decreasing and
constant failure rates.  (Actually for most distributions the failure
rate is decreasing for some values of t  and increasing for others.)
Consider the U(0,1) distribution and the exponential distribution with
mean 1.  Which of the following is true? 

(i) The exponential is increasing and the uniform is increasing. 
(ii) The exponential is decreasing and the uniform is increasing. 
(iii) The exponential is decreasing and the uniform is decreasing. 
(iv) The exponential is constant and the uniform is increasing. 
(v) The exponential is constant and the uniform is decreasing. 
(vi) The exponential is increasing and the uniform is constant. 
(vii) The exponential is decreasing and the uniform is constant. 
(viii) None of the above is true.


QUESTION -ext .R -run 'Rscript ./omsi_answer5.R'

(R code answer - 20 pts) A random variable X has density 
f_X(t) = c /(1+t^2) and support [-5,5], where c is the normalizing constant. 
Write a function to compute cdf F_X(t).

(Hint : use R function " integrate( function(x){ ____ }, __ , __ )$value " for integration)

F_X <- function(t){
  # compute "c" first
  c <-
  
  Ft <- 
} 

print(F_X(1))