Answer:
A) E(x) = n ( 1 - p ) = u ( 1 - 1 ) =0
B)
Step-by-step explanation:
In other to make money ( M ) you have to flip more head than tail
where : 0 < N < M
N = dollars in your pocket
M = money made from flipping the coin
<u>A) Show that with the probability one that the money in your pocket ends in a 0 or M as the game ends </u>
This is a binomial distribution problem hence to show that the money in your pocket ends in a 0 or M can be shown as
E(x) = np = u * 1
p = p( head )
1 - p = P ( tail ( failure ))
Hence
E(x) = n ( 1 - p ) = u ( 1 - 1 ) =0
<u>b) probability that the game ends with M dollars in your pocket </u>
To end up with M dollars you have to flip a head more often than a tail
P( head ) = p
P( tail ) = 1 - p
Hence the probability that the game ends with M dollars in your pocket
=
n = number of successions
p = probability of flipping a head
p-1 = probability of flipping a tail