A photon undergoes scattering events inside a dusty cloud before escaping

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Probability, statistics and stochastic methods · Probability, statistics and stochastic methods

Mathematical Methods for Physics, Ch Probability, random variables and distributions

Problem

A photon undergoes

k = 0, 1, 2, \ldots

scattering events inside a dusty cloud before escaping, with probability mass function

p(k) = \frac{C}{2^k}, \qquad k = 0, 1, 2, \ldots,

where

C

is a constant. ((a)) Find

C

. State why

p(k)

is a probability rather than a probability density, and give its units. ((b)) Find the probability that the photon escapes after two or fewer scatterings,

P(k \le 2)

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