A fair die is tossed until the first 1 appears. Let x equal the number of...
A fair die is tossed until the first 1 appears. Let x equal the
number of tosses required, x = 1,2,3,... You are to receive (.5)x
dollars if the first appears on the x-th toss. What is the expected
amount that you will receive? Hint: infinite geometric
series.
Homework Answers
P(1 on dice) = 1/6
E(x) = 1 / P(1 appearing)
= 1 / (1/6)
= 6
| E(ax) = a*E(x) |
amount recieved = 0.5*x
E(amount)
= E(0.5x)
= 0.5*E(x)
= 0.5*6
= $3
(please UPVOTE)
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