Mode of a Continuous Distribution

The mode of a continuous distribution is the most probable valueof the random variable associated with the distribution. If we sketchthe probability distribution function againstitwill typically have a maximum. Finding the mode then becomes a matterof 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 ifisincreasing then the mode is at the upper end of the range ofandifisdecreasing then the mode is at the lower range of the distributionof

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