Mode of a Continuous Distribution

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The mode of a continuous distribution is the most probable value of the random variable associated with the distribution. If we sketch the probability distribution function againstit will typically have a maximum. Finding the mode then becomes a matter of finding the turning point, or solving the equation

Example: Find the mean of the probability given by

The Uniform distribution does not have a mode sinceeverywhere, except at the ends. Also ifis increasing then the mode is at the upper end of the range ofand ifis decreasing then the mode is at the lower range of the distribution of

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