Please solve this stats problem...

[blinky8225]

Originally posted by: KoolAidKid

Originally posted by: blinky8225
I get 9800.

Let Q = quantity and C = Cost

Corr(Q,C) = 0.3 = Cov(Q,C)/(10 * 20) ==> Cov(Q,C) = 60

Var(10Q - C) = Var(10Q) + Var(C) + 2Cov(10Q,C) = 100Var(Q) + Var(C) - 20Cov(Q,C)
=100 * 100 + 400 - 20 * 60 = 9800

All the formulas used can be found on wikipedia or derived using the definition of Variance and Covariance.

Edit: I forgot a negative sign.

10000 + 400 - 1200 = 9200

Haha, ouch. Thanks for catching that mistake. Must have put it in wrong in my calculator, although, I really shouldn't need one for that calculation.

 

[slayer202]

not sure why you are using that equation and not the one I'm using
http://upload.wikimedia.org/ma...046e58b14d7a970f6b.png

 

[Born2bwire]

Originally posted by: slayer202
not sure why you are using that equation and not the one I'm using
http://upload.wikimedia.org/ma...046e58b14d7a970f6b.png

They are using your equation.

 

[slayer202]

Originally posted by: Born2bwire

Originally posted by: slayer202
not sure why you are using that equation and not the one I'm using
http://upload.wikimedia.org/ma...046e58b14d7a970f6b.png

They are using your equation.

this problem is killing me i swear. can anyone explain what I did wrong in my OP?

 

[blinky8225]

I'm just showing you how your equation is derived.

 

[Born2bwire]

Originally posted by: slayer202

Originally posted by: Born2bwire

Originally posted by: slayer202
not sure why you are using that equation and not the one I'm using
http://upload.wikimedia.org/ma...046e58b14d7a970f6b.png

They are using your equation.

this problem is killing me i swear. can anyone explain what I did wrong in my OP?

Var(10*Q+(-1)*C) = 10^2*Var(Q) + (-1)^2*Var(C) + 2*10*(-1)*Cov(Q,C) = 9200

 

[blinky8225]

100^2(100) + 980^2(400) - 2(100)(980)(.3)(10)(20)
Using your equation, you plugged into it
a = 100
b = 980
Unfortunately, those are the wrong values.
You want to find the expectation of Profit = 10*Q + (-1)*C
Therefore,
a = 10
b = -1

 

[slayer202]

Originally posted by: blinky8225
100^2(100) + 980^2(400) - 2(100)(980)(.3)(10)(20)
Using your equation, you plugged into it
a = 100
b = 980
Unfortunately, those are the wrong values.
You want to find the expectation of Profit = 10*Q + (-1)*C
Therefore,
a = 10
b = -1

ya know, I tried that during the test but I thought the number was still too high to be logical so I went with what I did first. damn...

I probably used 1 and not -1 though...

 

[blinky8225]

Originally posted by: slayer202

Originally posted by: blinky8225
100^2(100) + 980^2(400) - 2(100)(980)(.3)(10)(20)
Using your equation, you plugged into it
a = 100
b = 980
Unfortunately, those are the wrong values.
You want to find the expectation of Profit = 10*Q + (-1)*C
Therefore,
a = 10
b = -1

ya know, I tried that during the test but I thought the number was still too high to be logical so I went with what I did first. damn...

I probably used 1 and not -1 though...

Well if you think about it, take the square root of the variance you get. It's about $100. Therefore, ~70% of the time, profit will within $100 of the mean of 20, which really isn't too crazy.

 

[slayer202]

Originally posted by: blinky8225

Originally posted by: slayer202

Originally posted by: blinky8225
100^2(100) + 980^2(400) - 2(100)(980)(.3)(10)(20)
Using your equation, you plugged into it
a = 100
b = 980
Unfortunately, those are the wrong values.
You want to find the expectation of Profit = 10*Q + (-1)*C
Therefore,
a = 10
b = -1

ya know, I tried that during the test but I thought the number was still too high to be logical so I went with what I did first. damn...

I probably used 1 and not -1 though...

Well if you think about it, take the square root of the variance you get. It's about $100. Therefore, ~70% of the time, profit will within $100 of the mean of 20, which really isn't too crazy.

ya :/ not sure why but I was thinking it should have been smaller. damn! too bad, the next question was finding the probability that profits would be negative. I had to make up a standard deviation so that I could work it out for partial credit. Looks like the answer should have been .5 minus the zscore of -.2

 

[FelixDeCat]

Originally posted by: FelixDeKat
$6

price 10 x 100 = 1000
cost -980
----
Diff 20

20 x .03 = $6 (+/-)

So my answer of $6 was close to the answer of $10? Pshaw.