A number q is called a mode of a continuous distribution with a density f (x) if

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A number q is called a mode of a continuous distribution with a density f (x) if f (x) attains its maximum at q. (So, q may be called the most probable value.)

(a) Does a mode have to be unique? If not, give an example.

(b) Find a mode for the normal, exponential, and Γ-distribution.

(c) Find a mode for the uniform distribution.

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