Application of Probability to Mechanical Design
assuming each has the same probability regardless of arrangement
P(2A in 5 card) = IOP(AANNN)
P(AANNN) = P(A)P(A/A)P(N/AA)P(N/AAN)P(N/AANN)
P(A) = 4/52
P(A/A) = 3/51 with three aces still in the deck
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P(N/A, A) = ~ any card minus two aces
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P(N/A, A, N) =
46
P(N/AANN) = 4-~
= [~ 0.0399
(1 chance/25 trys)]
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IV. VARIANCE
A. Total Differential Estimate of the Variance
In this discussion some of the statements from 2.18-2.24] are stated without
proof and it should be noted sample sizes are infinite. A function ~ (x, y, z,
...) with a total differential of
~i- ~ = +~-- ~ + ~ + +~z.
~.~
oy
Oz
Has the estimate of the variance ~ as
Z(a~) 2
2~ -(2.13)
(2.14)
if xi and Yi are independent
~(ax~ay3 =
(O~) ~(6yi) 2
(2.15)
k~
n