The mode of a continuous distribution is the value x that maximizes f (x) a What is the mode of a normal distribution with parameters m and s b Does the uniform distribution with parameters and have a single mode Why or why not c What is the mode of an exponential distribution with parameter (Draw a picture ) d If X has a gamma distribution with parameters and , and 1, find the mode ln f(x) will be maximized iff f(x) is, and it may be simpler to take the derivative of ln f(x) e What is the mode of a chi squared distribution having n degrees of freedom

Question: The mode of a continuous distribution is the value x* that maximizes f (x). a. What is the mode of a normal distribution with parameters

The mode of a continuous distribution is the value x* that maximizes f (x).

a. What is the mode of a normal distribution with parameters m and s?

b. Does the uniform distribution with parameters μ and θ have a single mode? Why or why not?

c. What is the mode of an exponential distribution with parameter λ? (Draw a picture.)

d. If X has a gamma distribution with parameters α and β, and α > 1, find the mode. ln[f(x)] will be maximized iff f(x) is, and it may be simpler to take the derivative of ln[f(x)].

e. What is the mode of a chi-squared distribution having n degrees of freedom?

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