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) Why do we need the 1/(sqrt(2 pi) * sigma) factor in
the normal density?  After all, without it, we still have a bell-shaped
curve.

QUESTION

(Text answer - 20 points.)  Say we have data on people, and for each
person we have H, the proportion of their income that goes to housing.
Which one of our distribution families would be reasonable to explore as
a possible model for this data?

QUESTION

(Text Answer - 20 Points) For a gamma-distributed random variable X, which
is true about P(X has an integer value)? 

(i) 0
(ii) 1
(iii) infinity
(iv) depends on the value of lambda
(v) depends on the value of r
(vi) depends on the value of t
(vii) depends on EX
(viii) depends on Var(X)
(ix) none of the above is true

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

(R code answer - 20 Points)  Suppose W has a beta distribution for general
alpha, beta, t and u.  Evaluate both sides of Eqn. (8.9).

betamem <- function(alpha,beta,t, u) {



    return(list(lhs=lhs,rhs=rhs)  # left-hand and right-hand sides
}

print(betamem(1,1.8,0.5,0.2)

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

(R code answer - 20 Points)  Consider the power law family, Sec. 4.6.  We had
no "d/p/q/r" functions for that family.  Write the "d" function.  (Use
the approximate value of c.)

dpower <- function(gamma,k)  # k any pos. integer
{
}

print(dpower(2.0,3))