140. 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 A and B have a single mode? Why or why not?

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

d. If X has a gamma distribution with parameters a and

b, and a 1, find the mode. [Hint:

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?