August 2007 Question

[jamesy628]

I guess these two problems were very popular. It showed up on your August 2007 exam, showed up on the September 2007 exam (from other forum posters) and showed up on both November 2007 and February 2008 (both times when I took the exam).

And it tripped me up twice! So, if they decide to put these questions on AGAIN, I'll now be ready for them

[mcs84]

It would be nice to see the exact wording of the problem but it sounds like the payments start at 50, so yeah there would be a payoff of 0 for 49.999 inches of rain.

[iamsammy84]

For the rainfall problem. since it said every full 10 inches after 40 inches. does that mean you will start expected value 50 inches*whatever the probability+ etc.? thank you

[iamsammy84]

sorry once again..this question is really bugging mee.and im probably doin the same to u haha...but a quick question..why was male nonsmoker irrevelent?? thank you!

[rjkst14]

to rjkst14,

sorry for not understanding but why is female and male and smoker 0? and all the other 2 parts of the venn diagram 0?? thank you in advance!

well just read what you said.

the probability of being male and female and a smoker.

you can be either male or female, but not both. so the probability of being male and female and anything is going to be 0.

and the other one is the probability of being a smoker and not female and not male. and you have to either be a male or a female to be a smoker. so that probability is 0 as well.

hope this helps

[iamsammy84]

confused

to rjkst14,

sorry for not understanding but why is female and male and smoker 0? and all the other 2 parts of the venn diagram 0?? thank you in advance!

[rjkst14]

cant remember what it asked. but from looking at what i wrote i would guess the question was how many female smokers are there

[iamsammy84]

question

So what does the question about the smoker and females and males ask? what does 50 equal to? number of females?? thank you

[djerry81]

i had this question aswell.

i think the question said. there are 350 smokers, 150 more males then females and 100 more female nonsmokers then male nonsmokers.

First made the circles overlapping each other. (brain freeze cant remember the name of this)

each circle represented male, female and smoker

pr(smoker and not female or male ) = 0
pr( male and female and nonsmoker) = 0
pr(male and female and smoker) = 0

then i set male and nonsmoker as X
female and nonsmoker would then be 100 + x
male i set to 150 + y
female i set to y

once i had that set up i realized being a male and nonsmoker which i had as X was irrelivent so i put a 0 for that so female nonsmoker was just 100. then i could easily see to put 50 into female smokers and 300 into male smokers.

smokers = 350, 50 females and 300 males
males = 150 + "females" females was just 100 nonsmokers + 50 smokers
so males = 150 + 150 = 300
300 males = 0 nonsmokers and 300 smokers

answer is 50.

sorry if its hard to follow, but thats how i did it.

just make the diagram and you will see what i meant.

I almost used the venn diagram, like you did with this problem......I used tables which couldnt make since of, causing me to guess on the answer

[RobLin]

I thought that since you receive a payment once the rainfall hits 50 inches, the the expectation would start with .02 x 300 + ..... I believe though on the exam that the ranges were like this, with the "or equal to" part in front of the x.

Inches of Rainfall Probability
10 <= x < 20______.06
20 <= x < 30______.05
30 <= x < 40______.04
40 <= x < 50______.03
50 <= x < 60______.02
60 <= x < 70______.01

Now that I think about it, I really do agree with Chitown.. you have to start from 50-60 inches since they specifically indicated that for every full 10 inches in exceed of 40... which means that the payment doens't start from 50 and above... Things like this, you just wont' be able to catch it if you don't think CLEARLY enough..:skeptical:

[rjkst14]

There were two particular questions that I remember I had trouble with.

The first was something about a large pool of people that were divided into Males, Females, Smokers, and Nonsmokers. We were given that there were 350 total Smokers, 150 more female Nonsmokers compared to male nonsmokers, and then also given another bit of information which I do not remember. Does anyone recall this question and how they solved it?

Thanks.

i had this question aswell.

i think the question said. there are 350 smokers, 150 more males then females and 100 more female nonsmokers then male nonsmokers.

First made the circles overlapping each other. (brain freeze cant remember the name of this)

each circle represented male, female and smoker

pr(smoker and not female or male ) = 0
pr( male and female and nonsmoker) = 0
pr(male and female and smoker) = 0

then i set male and nonsmoker as X
female and nonsmoker would then be 100 + x
male i set to 150 + y
female i set to y

once i had that set up i realized being a male and nonsmoker which i had as X was irrelivent so i put a 0 for that so female nonsmoker was just 100. then i could easily see to put 50 into female smokers and 300 into male smokers.

smokers = 350, 50 females and 300 males
males = 150 + "females" females was just 100 nonsmokers + 50 smokers
so males = 150 + 150 = 300
300 males = 0 nonsmokers and 300 smokers

answer is 50.

sorry if its hard to follow, but thats how i did it.

just make the diagram and you will see what i meant.

[Chitown26]

I thought that since you receive a payment once the rainfall hits 50 inches, the the expectation would start with .02 x 300 + ..... I believe though on the exam that the ranges were like this, with the "or equal to" part in front of the x.

Inches of Rainfall Probability
10 <= x < 20______.06
20 <= x < 30______.05
30 <= x < 40______.04
40 <= x < 50______.03
50 <= x < 60______.02
60 <= x < 70______.01

[djerry81]

dJerry81, would you please explain how you were able to just take the amounts and probabilities to find Var(X)?

So, we were given something like (I am making up the probabilities):
Inches of Rainfall Probability
10 < x <= 20______.06
20 < x <= 30______.05
30 < x <= 40______.04
40 < x <= 50______.03
50 < x <= 60______.02
60 < x <= 70______.01

Since the payment, Y, is discrete, and the rainfall, X, seems to be continuous...Do you still multiply the appropriate probability with the dollar amount?

For example, to calculate the expected payment, E(Y) = .03 * 300 + .02 * 600 + .01 * 700 + ...

Thank you.

Sorry for not being so clear LOL but I skipped a bunch of steps........First find expected payment or E[X] then E[X^2]....starting with 50in
just as you have done above then plug into the variance formula and then viola.

I want to also point out to do you that you that on the May exam there were questions were given only enough information to calculate Cov from the definition. I know this problem was not like that but I just wanted to make you all aware that you could find according to definition only.

[crystal0]

Originally Posted by djerry81

I had trouble with the first one too. The second question I had, it was to find the std of the expected payment. We were given that for every full 10 inches above 40 the farmer would recieve $300 with a cap at 700. Now that means at 50 inches he gets 300, 60 inches 600, 70 inches 700, 80 inches 700 and I believe the probabilty of 90 or greater was zero so we didnt have to calculate this. with that I took the amounts and probabilities and found the Var(X) to calculate the answer

dJerry81, would you please explain how you were able to just take the amounts and probabilities to find Var(X)?

So, we were given something like (I am making up the probabilities):
Inches of Rainfall Probability
10 < x <= 20______.06
20 < x <= 30______.05
30 < x <= 40______.04
40 < x <= 50______.03
50 < x <= 60______.02
60 < x <= 70______.01

Since the payment, Y, is discrete, and the rainfall, X, seems to be continuous...Do you still multiply the appropriate probability with the dollar amount?

For example, to calculate the expected payment, E(Y) = .03 * 300 + .02 * 600 + .01 * 700 + ...

Thank you.

[sohpmalvin]

There were two particular questions that I remember I had trouble with.

The first was something about a large pool of people that were divided into Males, Females, Smokers, and Nonsmokers. We were given that there were 350 total Smokers, 150 more female Nonsmokers compared to male nonsmokers, and then also given another bit of information which I do not remember. Does anyone recall this question and how they solved it?

I got this also. The answer was 50.