By William Feller

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Extra resources for An Introduction to Probability Theory and Its Applications, Vol. 2

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B) The probability that it leads a platoon of total size n (with exactly n - 1 cars trailing it) tendS' to I/(n+l)(n+2). ' 11. Generalizatio~16 of the record value example 5(a).

To see this consider the axis NS of the sphere and the triangle NPS which has a right angle at P and an angle, at N. The length of NP is then 2, cos 0. 10 RANDOM DIRECTIONS 31 line NP into the diameter NS, and therefore cos E> is uniformly distributed' in 0, 1. " The resulting absorption of light was used as one example for the random-splitting process in the last section. ). (b) Circular objects under the microscope. Through a microscope. one observes' the projection of a cell on the Xl, x2-plane rather than its actual shape.


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