Thread: 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

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 ___.

that really helped,thanks alot

it ends up to 16, right?

any clue about (b)?

Originally Posted by parallel

that really helped,thanks alot

it ends up to 16, right?

...

hmm...I get 14

yea it's 14 , 2+4+8=14 (I made a stupid mistake)