# The shelf life, in days, for bottles of a certain prescribed medicine is a random variable

**ASSIGNMENT : **

[NOTE: The assignment is to be done entirely BY HAND]

1. ** **The shelf life, in days, for bottles of a certain prescribed medicine is a random variable having the density function

a) Find the value of A.

b) Find the probability that a bottle of this medicine will have a shelf life of anywhere from 80 to 120 days.

c) Find the average shelf life.

2. Consider the logistic equation (section 9.5) which is an equation of the form

** ( **constants**)**. (1)

First separate the variables in Eq. (1) and then derive the solution

** (2)**

that satisfies the initial condition **. If **** and ****are positive **

constants, then **. Hence then parameter **** in (1) is the ***limiting*

* population.*

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