Solved: The mode of a continuous distribution is the value

Chapter 4, Problem 111E

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Problem 111E

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 μ and σ ?

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 λ? (Draw a picture.)

d. If X has a gamma distribution with parameters α and β , and α >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 degrees of freedom?