3.8 You want to design an experiment where you simulate bacteria living in a certain medium. To this end, you know that the lifetime of one bacterium is a random variable X (in hours) distributed with exponential density 1 2 e−x/2. However, you also know that all of these peculiar bacteria live at least 1 h and die after 10 h. Thus you need to restrict the generated numbers to the interval (1, 10) by using a conditional density.

(a) Give the exact distribution (or density function) for a random variable which you may use to generate such numbers.

(b) Use any method and write a code in any programming language that allows you to generate random numbers with this particular conditional density