The reaction time (in seconds) to a certain stimulus is a continuous random variable with pdf

a. Obtain the cdf.

b. What is the probability that reaction time is at most 2.5 sec? Between 1.5 and 2.5 sec?

f(x) 5 •

3 2

# 1 x2 1 # x # 3 0 otherwise

(mm)

P(.5 # X # 2)

c. Compute the expected reaction time.

d. Compute the standard deviation of reaction time.

e. If an individual takes more than 1.5 sec to react, a light comes on and stays on either until one further second has elapsed or until the person reacts (whichever happens first). Determine the expected amount of time that the light remains lit. [Hint: Let h(X) the time that the light is on as a function of reaction time X.]