# probability (eating birds)

• Mar 10th 2007, 07:39 AM
parallel
probability (eating birds)
hello,I'm studying for an exam,and I need some help with this one:

assume that the time units are discrete:

there are 3 birds A B & C,at each time unit a bird can eat or guard,with probability 1/2 independently from the other birds,or her previous action.
at each time unit a hawk arrives,and if there is not 1 guard at least ,he randomly eats one of the birds.

a)if X is a random variable which counts the time it took for the hawk to eat all the 3 birds then E(X)=?
b)if the hawk didn't eat bird A first then her expected life span is?

help would be appreciated..thanks
• Mar 11th 2007, 08:59 PM
JakeD
Quote:

Originally Posted by parallel
hello,I'm studying for an exam,and I need some help with this one:

assume that the time units are discrete:

there are 3 birds A B & C,at each time unit a bird can eat or guard,with probability 1/2 independently from the other birds,or her previous action.
at each time unit a hawk arrives,and if there is not 1 guard at least ,he randomly eats one of the birds.

a)if X is a random variable which counts the time it took for the hawk to eat all the 3 birds then E(X)=?
b)if the hawk didn't eat bird A first then her expected life span is?

help would be appreciated..thanks

Here are some fill-in-the-blanks study questions intended to lead you to the answer for (a):
1. The hawk eating the birds represent _________ trials with parameters (success probabilities) p1, p2 and p3 depending on the number of birds. The values for these parameters are ___, ___ and ___.
2. The waiting time for a hawk to successfully eat a bird when there are k birds is a random variable Xk with a _________ distribution with parameter ___. The mean of this distribution is ___.
3. The time X it takes to eat all three birds is the sum of the three random variables X1, X2 and X3. The mean of a sum of random variables equals ___ ___ __ ___ _____. So the mean of X is ___.
• Mar 12th 2007, 02:12 AM
parallel
that really helped,thanks alot :)

it ends up to 16, right?

• Mar 12th 2007, 04:38 AM
frenzy
Quote:

Originally Posted by parallel
that really helped,thanks alot :)

it ends up to 16, right?

...

hmm...I get 14
• Mar 12th 2007, 06:36 AM
parallel
yea it's 14 , 2+4+8=14 (I made a stupid mistake)