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 and ? 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 ? (Draw a picture.) d. If X has a gamma distribution with parameters and , and 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? 1

Standardization of Turnip Peroxidase Enzyme f(x) = 0x + 0.21 f(x) = 0x + 0.1 f(x) = 0x + 0.06 0.5 mL Extract Linear (0.5 mL Extract) 1.0 mL Extract Linear (1.0 mL Extract) 2.0 mL Extract Linear (2.0 mL Extract) Effect of Temperature on Turnip Peroxidase Enzyme f(x) = 0.01x + 0.18 f(x) = 0.01x + 0.12 f(x) = 0x + 0.13 f(x) = 0x + 0.1 0 ºC Linear (0 ºC) 24 ºC Linear (24 ºC) 33.5 ºC Linear (33.5 ºC) 53 ºC Linear (53 ºC) 75.5 ºC Linear (75.5 ºC)