- Modified Jeopardy
Name that
Continuous
Distribution
Rules for
Expectations
Convergence
Related
Name that
Discrete
Distribution
Xforms of
All Types
100
100
100
100
100
200
200
200
200
200
300
300
300
300
300
400
400
400
400
400
500
500
500
500
500

What distribution might be appropriate for
jointly modeling test scores for two exams
where each exam’s marginal distribution was
symmetric?

What distribution would be appropriate to
model the proportion of voters who favor a
candidate?

What distribution would be appropriate for
modeling response times for a machine
where you expect most times to be short and
few to be large, where time is not measured
in discrete units?


What distribution might be appropriate for
modeling height of giraffes in zoos?
(Height is a common example where this
distribution occurs in practice).

This is the only continuous distribution with
the memoryless property and it also can help
model waiting time between Poisson events.

If X is independent of Y, Var(X)=2, and
Var(Y)=8, what is Var(6X+2Y)?

If Y has E(Y)=4 and SD(Y)=3, and X=4Y+9,
what are E(X) and SD(X)?

If X and Y are jointly distributed RVs,
Cov(X,Y)=0, E(X)=6, E(XY)=12, what is E(Y)?

Does Cov(X,Y)=0 imply X is independent of Y?

If Y has E(Y)=2 and SD(Y)=1 and X=Y^2-6Y+3,
what is E(X)? Is there enough information given
to get SD(X)?

X and Y are jointly distributed RVs with
correlation .5, V(X)=10, and V(Y)=6. What is
Var(2X-Y)?

The CLT is an example of this type of
convergence result.

If we have a random sample of n
observations, where E(X) and V(X) exist, then
X-bar converges in quadratic mean to this
value.

If X is Gamma(2,3), and we have a random
sample of 30 variables that behave like X,
what does X-bar converge in probability to?
How do you justify this?

If X is Poisson(6), then Y=X-6/sqrt(6)
converges in distribution to this distribution.

If X is from any unknown distribution with
E(X) and V(X) finite, what can you say about
the distribution of X-bar for a random sample
of 60 variables from X’s distribution?

What distribution would be appropriate to
model the number of trains arriving at an
Amtrak station in an hour if in the past year,
there have been 3 trains hour arriving, on
average, each hour?

What distribution would be appropriate to
model the number of times a person takes a
shot in basketball before making a total of
five baskets?

What distribution would be appropriate for
modelling the size of a population of wild
animals based on a capture-recapture
method?

What distribution would be appropriate for
modeling t-shirt sales for a store where there
are 4 shirt sizes, and they plan to order 900
shirts?

What distribution would be appropriate to
model the number of successful police stings
out of a fixed number of planned stings in a
given month assuming the stings are
independent?

If Y_1,Y_2,Y_3, and Y_4 are all Geometric(.7),
what distribution does the sum of the Y’s
have? (How do you know?)

If Y is Uniform(6,10), what are appropriate
methods to find the pdf of X=Y^2+6?

If X and Y are independent, each Exp(2), and
Z=X+Y, and W=X, what methods will give you
the joint density for Z and W?

If X and Y are independent Gamma RVs, what
methods exist to find the pdf of W=2X+3Y?

The neat matrix required to do the method of
2-D xforms.
Standardization
Fun
Pesky
Integrals
Probability
Basics
Anything
Conditional
Random
200
200
200
200
200
400
400
400
400
400
600
600
600
600
600
800
800
800
800
800
1000
1000
1000
1000
1000

The value you would compute if you wanted
to find P(X>16) when X was normally
distribution, mean 12, SD 4.

If X is Binomial (1000,.4), this is the method
you could use to approximate P(X>425).

The extra “boost” to any continuous
approximation of a discrete distribution,
designed to improve the approximation.

If X has mean 20 and standard deviation 2,
and we have a random sample of 36
observations from X’s distribution, this is
how you would find P(X-bar<19).

What are good values for n and p for the
Normal approximation to the Binomial, and
good values for lambda for the similar
approximation to the Poisson?

For this category, let X and Y denote random
variables with joint pdf given by
2 x
2e
f ( x, y ) 
x


Where 0<y<x< infinity
You may refer to the joint just as f(x,y) but
bear the bounds in mind for this category.

Setup an integral (or integrals) to find P(Y>5,
X>4)

Setup an integral (or integrals) to find P(Y<3,
X<6)

Setup an integral (or integrals) to find
P(X>2Y)

Setup an integral (or integrals) to find E(X)

Setup an integral (or integrals) to find E(XY)

These are the three axioms of probability.

If you are trying to carry 10 total objects and
you decide to give 2 randomly to a friend to
carry, this is the number of total object
arrangements your friend might end up with.

If license plates had to have the following
format (L=letter, N=number): LLNNLL, and
repeated letters and digits were not allowed,
how many possible license plates could be
made?

If you were asked for P(B|A) and all you had
was marginal info about B, B complement, A
given B, and A given B complement, this is
how you would find the desired probability.

If you have just taken a test for a rare disease
and received a positive test result, this is the
value you should focus on to determine the
probability you actually have the disease.

If X and Y are independent, then the pdf of X
given Y is equivalent to this pdf.

If X given Y is Normal(Y, 2), and Y is
Uniform(0,4), then E(X) is equal to this value.

If X given Y is Normal(Y, 2), and Y is
Uniform(0,4), then V(X) could be found by
computing this expression (or using this
technique)

Three prisoners are up for parole, but only 2
will get it. Prisoner C asks a guard for the
name of one of the prisoners who is going to
be paroled. The guard says “Prisoner A”.
Prisoner C is very unhappy as his chances of
parole are now ½ instead of 2/3 because
either he or prisoner B will get released in
addition to A. What if anything is wrong with
Prisoner C’s reasoning?

The conditioning method of xforms relies on
the fact that a joint pdf can be rewritten as
this product.

A Markov chain with 3 absorbing sets in
addition to the entire sample space is called
this.

If X is Uniform(0,100), this theorem could be
applied to find an interval in which 75% of the
distribution of X lies.

The only discrete distribution that is
memoryless


Bivariate normal random variables have
marginal distributions which have this
distribution.
(Note you don’t need these formulas, but
knowing the distribution is a neat fact.)

Martingales, Markov Chains, and Poisson
processes are all examples of this type of
process.



Final Exam is Saturday, December 18th, 2-5 in
Merrill 03
You can bring a two-sided page of notes and
calculator, plus pen/pencils.
Exam Week Office Hours:
◦ Wednesday 3-5
◦ Thursday 1-4
◦ Friday – 1-4

Good luck studying!
 Remember
Math dept. end of
semester party is today from 3:30
– 4:30 in SM 208!



You should be able to access the evaluations
online from the course website.
I cannot see what you enter there, and will
only see it after grades are entered and with
names removed.
DO NOT HIT ENTER as you type through it as
that submits the form. You must use TAB or
the mouse to move between fields. (I didn’t
set this up.)