Joe will roll a pair of dice until he rolls a 7 (sum of 2 numbers). Let X be number of times he will roll without getting a 7.
(For example, if on the third roll Joe first rolls 7, then X=2.)
What is the expected value of X?
[hints:
let p(x) denote probability that X=x.
The expected value will be an infinite series, (0)p(0) + (1)p(1) + (2)p(2) + ... .
After the formula for p(n) is determined, compute the series (remember 1 + x + x^2 + x^3 + ... = 1/(1-x), if |x|<1)
Take the derivative of both sides.
]
2007-07-25
22:20:02
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3 answers
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asked by
Anonymous