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

f(x) = k/x² , 1x4; f(x) = 0, otherwise

1. Determine the value of k.
2. Obtain the cdf.
3. What is the probability that reaction time is at most 3 sec? Between 2 and 3 sec?
4. Compute the expected reaction time.
5. Compute the standard deviation of reaction time.
6. An individual accepts stimulus from a light which comes on and stays on for two seconds. If the person doesn't react in the first two seconds, the light stays until the person reacts. 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.]