Question from exam

[iamsammy84]

If a question asks you there is a max limit of 3000. and is exponential distributed w/ mean equal some number (i forget).
If they ask you what is the probability of an insurance company paying exactly 3000? how would u solve a problem like that?

Another question:

something is poisson distributed w/ mean 2. and a company pays each benefit 3000. with a max of 3 benefits. What is the standard deviation?

Another question:

There was a problem giving probability of something increasing, decreasing or staying the same. And then they gave another table giving hte probability of increasing, decreasing of staying hte same. and they ask you which is true? does anyone remember a question like that? and the answers were variance of x is greater than variance of y and the mean r the same, and so forth? (sorry i do not remember exactly...)

Another question:

there was a problem that gives f(x,y)= 1/2 and x= 0,1,2,3,4 and y=0,,,,,,x
Does anyone recall that problem??

Thank you in advance

[jstarderfan]

I will answer the first three after I am done celebrating...the fourth:I didn't have that one; I need more info.

[jthias]

The last one is x=0,1,2,...,5; y=0,1,2,...,x

p(x,y) is given and you are asked to find V(Y).

You basically set up a triangular ''''' using the domain values of p(x,y), then use the sum of the number of entries in the jth column to determine the marginal probability of Y = j. Then you just use the marginal probability function of Y to compute V(Y).

[aminesky]

Hey jthias,

Exactly, I had the same question regarding the policy paying 3000...I don't recall exactly the parameter of the exponential that was given. But the question stated something in the lines with: The losses are represented by an exponential with mean theta (given) and there is a deductible of 1000. The maximum benefit is 3000. What is the probability that the insurer pays exactly 3000.

What they looked for is in fact the probability of the loss being higher than 4000. Since there is a deductible of 1000 (1000 + 3000 = 4000).

P(loss => 4000) = int(from 4000 to infiniti) f(x) dx. That was simply s(x). They wanted you to calculate the probability that the incured loss was 4000 or higher so that the insurer pays 3000, the max benefit.

Hope that might help,
aminesky

[anajm]

For the problem with max benefits of 3. I think the qusetion is the expected payout. whether it is E(x), V(x), or the std diviation it doesn't matter. I suppose the amount of one benefit was 10, since the number of storms follows Poisson and only 1 benefit a year over the next 5 years. then I think it will be written like that.

E(x) = 0P(0) + 10P(1) +20 p(2)+ 30P(3) +30 P(4) + 30 P(5)

Wher P(n) = e^(-Lambda)(Lambda^n)/n!

[jthias]

Hey jthias,

Exactly, I had the same question regarding the policy paying 3000...I don't recall exactly the parameter of the exponential that was given. But the question stated something in the lines with: The losses are represented by an exponential with mean theta (given) and there is a deductible of 1000. The maximum benefit is 3000. What is the probability that the insurer pays exactly 3000.

What they looked for is in fact the probability of the loss being higher than 4000. Since there is a deductible of 1000 (1000 + 3000 = 4000).

P(loss => 4000) = int(from 4000 to infiniti) f(x) dx. That was simply s(x). They wanted you to calculate the probability that the incured loss was 4000 or higher so that the insurer pays 3000, the max benefit.

Hope that might help,
aminesky
I remember that one...don't recall if I got it right...seems easy enough though. I agree with your approach.

If X is loss amount and Y is benefit amount with deductible d=1000, then

Pr(insurer pays 3000) = Pr(X-d > 3000) = Pr(X>4000) = S_x(4000).

By the way, is it ok to post exam problems AFTER the exam, or similar problems, anyone know?

[Tara in Chicago]

I did not get this problem either...the 4th one listed at the top.

I do not understand how you set it up like that. What is the p(0,0) or p(1,0) to start? How would you sum the marginal probabilities for E(Y), E(Y^2), to find V(Y)?

[jthias]

Problem is shown below..couldn't get domain values to appear correctly.

[jthias]

Here's one sorta similar to one of the exam problems.

p(x,y) = 1/8 for X=0,1,2,....,y^2; Y=0,1,2

Find the coefficient of variation of Y.




First, the key step, set up the ''''' of possible domain values for the joint probability function.

00 01 02
----11 12
--------22
--------32
--------42

Then calculate the marginal probabilities of Y.

p_Y(0) = 1/8

p_Y(1) = 2/8

p_Y(2) = 5/8


Find the coefficient of variation of Y.

E(Y) = 0(1/8) + 1(2/8) + 2(5/8) = 3/2

E(Y^2) = 2/8 + 4(5/8) = 22/8

V(Y) = 1/2

The coefficient of variation is sqrt(V(Y))/E(Y) = [1/sqrt(2)]/(3/2) = sqrt(2)/3.

[jthias]

Or we could do another variation on the problem.

p(x,y) = 1/10 for X = 0,1,4,9
and Y = 0,1,2,...,sqrt(x)

Find the standard deviation of X.

Set up the ''''' of possible domain values (you should have 10 of them since p(x,y) is uniform on the discrete "region")

00
10 11
40 41 42
90 91 92 93

p_X(0) = 1/10
p_X(1) = 2/10
p_X(4) = 3/10
p_X(9) = 4/10

p_X(x) is 0 otherwise for values of x not 0,1,4 or 9.

E(X) = 2/10 + 4(3/10) + 9(4/10) = 5
E(X^2) = 2/10 + 16(3/10) + 81(4/10) = 37.4

V(X) = 12.4

Standard deviation is appoximatey 3.52

[anajm]

I did not get this problem either...the 4th one listed at the top.

I do not understand how you set it up like that. What is the p(0,0) or p(1,0) to start? How would you sum the marginal probabilities for E(Y), E(Y^2), to find V(Y)?

E(x) = 0P(0) + 1p(1) +3P(3) + 4P(4)
P(0) =P(0,0)= 1/3
P(1) = p(1,0) +P(1,1)=2/3
P(2)= P(2,0) + P(2,1) + P(2,2).....etc

[Durh]

I did not get this problem either...the 4th one listed at the top.

I do not understand how you set it up like that. What is the p(0,0) or p(1,0) to start? How would you sum the marginal probabilities for E(Y), E(Y^2), to find V(Y)?

x goes from 0 to 5. y only goes to x. So if x=0, y=0. If x=2, y=0, 1, 2. For the same reason, if x=2, y cann't be 3 or higher. The table below summarizes the data. Say f(x, y)=1/8 if (x,y) is in the domain, f(x,y)=0 elsewhere. I'm just putting f(x,y)=p in the table, since I can't get the format I want if I put a number there. Anyway, p is a constant that is given in the question.

x= 0 1 2 3 4 5
-------------------------------------------
y=
0 p p p p p p

1 0 p p p p p

2 0 0 p p p p

3 0 0 0 p p p

4 0 0 0 0 p p

5 0 0 0 0 0 p

Now you know how to calculate E[y] and E[y^2], just like how you would deal with a regular table. I guess this the triangle jthias had in mind, at least I hope.

[anajm]

In my reply I took x =0,....,y and y=0,...3 and not the other way around.:smiloe:

[jthias]

In my reply I took x =0,....,y and y=0,...3 and not the other way around.:smiloe:
I think you had it right originally as x = 0,1,2,3 and y = 0,1,2,...,x

we get the '''''

00
10 11
20 21 22
30 31 32 33
Then we get p_X(1)= 2/10, but what you have is the following ''''' for y=0,1,2,3 and x=0,1,2,...,y

00 01 02 03
----11 12 13
--------22 23
------------33

Which give us p_X(1) = 3/10

[jthias]

I think I see a triangle in there somewhere Durh ;)

[Durh]

I think I see a triangle in there somewhere Durh ;)

Sure, I see it too. It's nice.:smiloe:

[Ken]

You
Can
Get

everything to line up if you wrap it in code tags.

[Durh]

You
Can
Get

everything to line up if you wrap it in code tags.

Ken, this is why my name is Durh. What code tags? Many thanks!

Durh

[jthias]

00 00 00 00
00 00 00
00 00
00

[jthias]

Ignore this post...testing code tags only



00 01 02 03
11 12 13
22 23
33


Got It, Thanks Ken!

[jthias]

When posting a message you have a bunch of tags on the 2nd row that affect the way any text typed between the tags is presented. The 2nd row of tags begins with "bold" tag on the left and ends with the "php" tag on the right. The code tag is 3rd from right and has # sign as its symbol.

[djerry81]

If a question asks you there is a max limit of 3000. and is exponential distributed w/ mean equal some number (i forget).
If they ask you what is the probability of an insurance company paying exactly 3000? how would u solve a problem like that?

Another question:

something is poisson distributed w/ mean 2. and a company pays each benefit 3000. with a max of 3 benefits. What is the standard deviation?

Another question:

There was a problem giving probability of something increasing, decreasing or staying the same. And then they gave another table giving hte probability of increasing, decreasing of staying hte same. and they ask you which is true? does anyone remember a question like that? and the answers were variance of x is greater than variance of y and the mean r the same, and so forth? (sorry i do not remember exactly...)

Another question:

there was a problem that gives f(x,y)= 1/2 and x= 0,1,2,3,4 and y=0,,,,,,x
Does anyone recall that problem??

Thank you in advance


I remember the increasing and decreasing question......It is a question from Probabilty for Risk management Chpt 4 I have the book at home I will post that question tomorrow it was what I believe the question your ask in regard to stocks increasing/decreasing due to the economy being stable increasing or decreasing. I was very surprised to see that question in the book already answered after I took the test.

[djerry81]

I remember the increasing and decreasing question......It is a question from Probabilty for Risk management Chpt 4 I have the book at home I will post that question tomorrow it was what I believe the question your ask in regard to stocks increasing/decreasing due to the economy being stable increasing or decreasing. I was very surprised to see that question in the book already answered after I took the test.

from Risk Management for Probability
Its a problem in Chapt 4.4.3 Comparing Two Stocks.....I can't reproduce this because of the author but I can give u the idea of it
Given Economy Probability

Increases .25
Unchanged .5
Deteriote .25



%Change in Stock A
increase .1
stable .05
decrease .1


% Change in Stock B
increase .15
stable .05
decrease .15

What can be said from the data above

Both E[x] and var(X) same
Ex and varx for A higher than B
ex and varx for A lower than B
EX for both same varx for A higher than B
EX for both same Varx for B higher than A


Something to that affect

[jthias]

Oh, I remember one similar to that one on the exam. I felt I got it right.

[djerry81]

Did you see the problem in the book it is the exact same problem in the book that was on the test

[jthias]

Yes, page 95.

[anajm]

Can someone post a solution for the problem posted which is said to be from the book. Plus could you please post the name of the book and whether it's useful for both exam 1 and 2.
Thanks,

[djerry81]

Can someone post a solution for the problem posted which is said to be from the book. Plus could you please post the name of the book and whether it's useful for both exam 1 and 2.
Thanks,

Its pretty simple give it a try....your being tested

Hint let X be the change in value of the stock and remember Var(X) is also E[(X-mean)^2]
happy solving

The book can be found here
http://www.actexmadriver.com/productdetails.cfm?PC=1427

This is in no way an advertisment for ACTEX just informational

[billvp]

I remember that problem on my exam-P also ... but didn't it also say that both stocks were currently worth the same amount?

[djerry81]

I remember that problem on my exam-P also ... but didn't it also say that both stocks were currently worth the same amount?

I didnt want to copy it but the same idea is in the problem and the same answer we are looking for also