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1.4: Continuous Probability Distributions

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Suppose 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 (1.2.4), (1.3.4), and (1.3.11) generalize in a straightforward manner to give: 1=P(u)du,u=P(u)udu,(Δu)2=P(u)(uu)2du=u2u2,
respectively.

Contributors and Attributions

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


This page titled 1.4: Continuous Probability Distributions is shared under a not declared license and was authored, remixed, and/or curated by Richard Fitzpatrick.

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