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 Points)  One can use a(n) ____________________________ to
estimate a density from data.

QUESTION

(Text Answer - 20 Points) 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 Points) The word "limit" in "Central Limit Theorem" alludes
to which of these?  
(i) n => infinity 
(ii) mu => infinity 
(ii) sigma => infinity 
(iv) t => infinity 
(v) n => 0 
(vi) mu => 0
(vii) sigma => 0
(viii) t => 0 
(ix) none of the above

QUESTION -ext .R -run 'Rscript ./omsi_answer4.R'

(R Code Answer - 20 Points) Consider the random variables N(t) in Sec. 8.1.
Suppose the X_i have a U(0,1) distribution, not exponential.  Find
P{N(t) = 0).

nt0 <- function(t)  # t can be any pos. number
{


}

print(nt0(0.6))
print(nt0(1.6))

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

(R code answer - 20 Points)  The hazard function for a random variable X is
defined to be f_X(t) / [1 - F_X(t)].  Write code for this for the
density 2t, 0 < t < 1.

haz <- function(t)
{


}

print(haz(0.5))