Practice problem (and RFSCDME support request)

[Gandalf]

Daily margins (M) in the Pillow – Tim>< match are identically 
and independently distributed with density

f(m) = k (m+5), -5 < m < 5, where m is Pillow’s margin for the day 

e.g., m=-2 means Tim>< gets 2 more votes than Pillow for the day.  
Treat M as a continuous random variable, so outcomes like 6.1 
are possible, even though actual votes are discrete.

1. Calculate k.
(A)	.01
(B)	.02
(C)     .03
(D)	.04
(E)	.05

2. Calculate Prob(M>3)
(A)	.20
(B)	.24
(C)     .28
(D)	.32
(E)	.36

3. Pillow trails by 2 at the end of day 2.  Only two days left to catch up!
Calculate the probability that Pillow wins.
(A)	.33
(B)	.42
(C)     .50
(D)	.67
(E)	1.05 

It's not likely that the probability in 3 could exceed 1,
but 1.05 is what I got when I first tried to solve the double integral.

)

Proposed answers

Spoiler:

1. B; integral of density must be 1 2. E 3. D (Let X be day 3 of voting; Y be day 4. Integrate f(x)f(y)dydx over the region where X + Y > 2.

[michael solomon]

I got .36 (ans E) for number 2. Am I definately wrong?

[Gandalf]

E looks right to me. I forget why I said D before. Maybe a typo?

No one challenged D before. Maybe no one worked it before.

[CamNZ]

Why do my double intergrals never, NEVER, end up with an answer matching A - E. I find the correct f(x,y), I set up a graph of the region, it takes friggen ages for an answer to drop out and when it finally comes, its not the answer at all, it's the answers retarded cousin! And it wouldn't suck so bad if it didn't take so long to find out that it's wrong, and then there's to many steps to retrace to find the error. Does any one else feel my pain?