Let X be a random variable that measures the age of a randomly selected cell in a particular population. Suppose X is distributed exponentially with a probability density function of the form

where x is the age of a randomly selected cell (in days) and k is a positive constant. Experiments indicate that it is twice as likely for a cell to be less than 3 days old as it is for it to be more than 3 days old.

a. Use this information to determine k.

b. Find the probability that a randomly selected cell is at least 5 days old.

Transcribed Image Text:

f(x): = -kx ke for x ≥ 0 otherwise