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2.5:Continuous Probability Distributions

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Suppose, now, that the variable u can take on a continuous range of possible values. In general, we expect the probability that u takes on a value in the range u to u+du to be directly proportional to du, in the limit that du0. In other words,

P(uu:u+du)=P(u)du

where P(u) is known as the probability density. The earlier results (5), (12), and (19) generalize in a straightforward manner to give

1=P(u)duu=P(u)udu(Δu)2=P(u)(uu)2du=u2u2

respectively.

Contributors

  • Richard Fitzpatrick (Professor of Physics, The University of Texas at Austin)


This page titled 2.5:Continuous Probability Distributions is shared under a not declared license and was authored, remixed, and/or curated by Richard Fitzpatrick.

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