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View Full Version : Need one last help b4 my exam tomorrow!! Please and thank you!!

browneyedgirl232
07-27-2011, 11:53 AM
I'm still a little confused about a couple concepts/questions and I'm sitting for the exam tomorrow so if someone would please help me clear up some of them it would be awesome! I'd give you a big hug if i could!!

1. ASM PE #1 is about finding the E(x) of max(x1,x2, x3, x4) blah blah blah, what if you are asked to find expected value of the two bigger values or two smaller values conbined instead of the biggest or smallest? (ie E(x1+x2) if x1 and x2 are the bigger ones of the four)

2. I'm really bad at those some type of prob questions...any advice? like what's the probability of that you get 3 same results if you throw a die 4 times.

3. When it says in the question that the insurance company covers up to xth percentile of the loss denoted by X. It means that Pr(X < x/100) correct?

4. another question about percentile. if you are asked to find xth percentile of a normal distribution variable. do you need to use Pr(x<x/100）and then transfer x into Z and then go from there?

Sorry i have a bunch of questions.. thanks in advance and hopefully i'll pass tomorrow!

Damascus
07-27-2011, 12:59 PM
Normally I would let someone smarter take this, but considering I'm taking this Friday, one would hope I could answer these questions...

1. No idea.... 1 more thing for me to study =)

2. Same number 3 times in 4 rolls would be 4 choose 3 possible combinations times (1/6)^3*(5/6) (3 successes and 1 failure)... and I'm pretty sure you multiply that by 6 because there are 6 possible numbers that you can choose to repeat... right? 5/54 is what I got... For these you can draw it out... I would draw 4 squares (to represent dice) and list some possibilities until I get the feel of it and can form some type of calc.

3. Percentile is (X<=x) = n-th. So 95th percentile is Pr(X<=x) = .95. So you need to solve for 'x'. Either integration of f(x) from -infinity to 'x' or use the CDF F(x)=.95.

4. Z is for approximating with normal distribution. If you want to find the n-th percentile of a uniform dist. you either integrate the density function f(x) from -infinity (or often 0) to x and set it equal to 'n' or use the CDF F(x)=n.

For example on 4. If we ask 40th percentile of UNIF(0,5). You do the integral of 1/5 from 0 to x and set it equal to .4. Then solve for 'x'

Kaner3339
07-27-2011, 01:08 PM
1. Order statistics. About the PE 1 quesiton, if I recall it's a max question with trig in it right and you want the expected value. When your talking max and min it's easy to know if the max is less than something and easy to know if the min is bigger than something. In either case you get the CDF or survival, and if u get the CDF the look at 1 minus that and you get the survival. then integrate for expected value. if you want other moments you need to get the pdfs. About expected values of other things like x1,x2, if you're talking order statistics then these are the two smallest values, then you need to know the formula for the nth order statistic and apply it.

2.look at the binomal distribution.

3.for percentile questions look at examples and you'll get the hang of it.

4. you don't always use z scores when talking percentiles. if you're talking a uniform distribution then just look at P(X<x) = p. Don't get stuck in the mindset it has to be normal because it doesn't.

Damascus
07-27-2011, 01:10 PM
I understand min's and max's but that's it about ordered statistics.

Damascus
07-27-2011, 01:31 PM
ooops, is that wrong for the dice problem? I'm not supposed to multiply by 6, am I?

I think I combined two approaches there.

Either you count all the "favored" outcomes and then divide by total possible outcomes, OR you do binomial distribution... I did a bit of both there...

*edit* Now I'm all confused... someone get Joni in here!

browneyedgirl232
07-27-2011, 01:39 PM
thank you so much!!
and for no.4 sorry I meant normal dist not uniform. and Im confused because Idk what to put for F(x)?

Normally I would let someone smarter take this, but considering I'm taking this Friday, one would hope I could answer these questions...

1. No idea.... 1 more thing for me to study =)

2. Same number 3 times in 4 rolls would be 4 choose 3 possible combinations times (1/6)^3*(5/6) (3 successes and 1 failure)... and I'm pretty sure you multiply that by 6 because there are 6 possible numbers that you can choose to repeat... right? 5/54 is what I got... For these you can draw it out... I would draw 4 squares (to represent dice) and list some possibilities until I get the feel of it and can form some type of calc.

3. Percentile is (X<=x) = n-th. So 95th percentile is Pr(X<=x) = .95. So you need to solve for 'x'. Either integration of f(x) from -infinity to 'x' or use the CDF F(x)=.95.

4. Z is for approximating with normal distribution. If you want to find the n-th percentile of a uniform dist. you either integrate the density function f(x) from -infinity (or often 0) to x and set it equal to 'n' or use the CDF F(x)=n.

For example on 4. If we ask 40th percentile of UNIF(0,5). You do the integral of 1/5 from 0 to x and set it equal to .4. Then solve for 'x'

Damascus
07-27-2011, 01:41 PM
4 ways to arrange, 5 possible outcomes for each combination, 6 possible numbers to choose...=120 over 6^4 =1296 120/1296=5/54 (by counting)

(4 choose 3) ways to arrange, (1/6)^3 success, (5/6)^1 failure = 20/1296... (by binomial dist.) So, binomial dist. only gives you the probability of 1 number coming up 3 times, not ANY number... Since there are 6 numbers, you have to multiply the binomial dist by 6 to compensate... 6*20/1296=120/1296=5/54....

Damascus
07-27-2011, 01:44 PM
n-th percentile for Normal is even easier... the CDF of Z is the table they always give you. So if they ask you 40th percentile of a normal distribution you just look at the table for the decimal closest to 0.4000 (may have to interpolate) and whatever Z that corresponds to is your answer.

So find 60th percentile of N(0,1) would be Pr(Z<=z)=0.6000. Z there is about .255 (you should approximate closer, but I'm lazy atm). So your answer is .255.

If they ask for N(E(X),Var(X)) you use E(X)+StdDev(X)Z. and plug .255 in for Z.

browneyedgirl232
07-27-2011, 01:48 PM
I need to go over order statistics I hardly know anything about it except max n min questions...
I don't remember where I saw this question but it was sth like PE #1 but instead of asking for max ( accepting the highest bid ) the company only pays for the two lower claims and you're asked to find E(what's covered by the policy.)

thank you and congrats on ur pass!!

1. Order statistics. About the PE 1 quesiton, if I recall it's a max question with trig in it right and you want the expected value. When your talking max and min it's easy to know if the max is less than something and easy to know if the min is bigger than something. In either case you get the CDF or survival, and if u get the CDF the look at 1 minus that and you get the survival. then integrate for expected value. if you want other moments you need to get the pdfs. About expected values of other things like x1,x2, if you're talking order statistics then these are the two smallest values, then you need to know the formula for the nth order statistic and apply it.

2.look at the binomal distribution.

3.for percentile questions look at examples and you'll get the hang of it.

4. you don't always use z scores when talking percentiles. if you're talking a uniform distribution then just look at P(X<x) = p. Don't get stuck in the mindset it has to be normal because it doesn't.

TheGillotine
07-27-2011, 01:58 PM
Order Statistics:
This is the formula you want to know

Jake_The_Snake_724
07-27-2011, 02:05 PM
I need to go over order statistics I hardly know anything about it except max n min questions...
I don't remember where I saw this question but it was sth like PE #1 but instead of asking for max ( accepting the highest bid ) the company only pays for the two lower claims and you're asked to find E(what's covered by the policy.)

thank you and congrats on ur pass!!

You might want to study that topic until you can do it in your sleep!

browneyedgirl232
07-27-2011, 02:12 PM
You might want to study that topic until you can do it in your sleep!

!! I didn't think order statistics is that important. could you explain to me the basic idea of how to solve this one? I'm still confused n can't find the original problem on ASM...
thank you!

Kaner3339
07-27-2011, 02:26 PM
!! I didn't think order statistics is that important. could you explain to me the basic idea of how to solve this one? I'm still confused n can't find the original problem on ASM...
thank you!

It's the very first question in the very first exam. and I haven't passed yet! doin it tomorrow!

browneyedgirl232
07-27-2011, 02:29 PM
It's the very first question in the very first exam. and I haven't passed yet! doin it tomorrow!

hehe yea I know how to do PE#1 to find max but how about the other similar question I posted?
I'm taking it tomorrow too.

Kaner3339
07-27-2011, 02:31 PM
the question about the expected value of E(X1 + X2) where X1 and X2 are the smallest?

browneyedgirl232
07-27-2011, 02:34 PM
the question about the expected value of E(X1 + X2) where X1 and X2 are the smallest?

yes. say the losses follow an exponential (or whatever other dist) with a given mean and the company only pays for the two lower claims and you're asked to find E(what's covered by the policy.)

Kaner3339
07-27-2011, 02:43 PM
Then use the pdf formula that Guillotine posted to find their pdfs, then integrate for their cfds and integrate the survival for the expected value. Or use the pdfs directly.

Sinkingfun
07-27-2011, 02:48 PM
i find with order statistics, it's pretty easy and important to memorize the basic formula:

(n!/{(i-1)!(n-i)!}) * (1 - F(n))^(n-i) * (F(n))^(i-1) * f(n).

where i is the ith one in the list...(i = 1 is the min and i = n is the max).

If you were looking for E(x1 + x2) ,

You could just do E(x1) + E(x2)

You know the densities of f i (n).

btw, an easy way to figure out F(n) out of the generic f(n) is to integrate f(n) from the lower boundary of n to some dumby variable.

Also, if the question asks you for a probability question concerning min's and maxes..like "What is the probability the min of all of these is less than 1?"

That is the same thing as 1 - P(all of them are greater than or equal to 1).

Likewise, if the question is "What is the probability that the max of all of these is less than 1?"

That is the same thing as P( all of them are less than 1).

If the question is "What is the probability that the min is greater than 1?"

that is the same as the prob that all are greater than 1.

Kaner3339
07-27-2011, 02:50 PM
Lol sinking, a much more visually appealing version of that formula is on the previous page.

Sinkingfun
07-27-2011, 02:53 PM
Lol sinking, a much more visually appealing version of that formula is on the previous page.

hahahaha that's hilarious. Woops.

browneyedgirl232
07-27-2011, 03:11 PM
thanks everyone! im off to more order statistics now.