1. Let,
(a)
Show that is a probability density function.
(b)
Find .
(c)
Find .
(d)
Find .
(e)
Determine the mean value of X.
2. Let,
(a)
Show that is a probability density function.
(b)
Find .
(c)
Find .
(d)
Find .
(e)
Determine the mean value of X.
3. Let,
(a)
Show that is a probability density function.
(b)
Find .
(c)
Find .
(d)
Find .
(e)
Determine the mean value of X.
4. The probability density function of the life span of a
battery is given by the function below, where t is in years.
(a)
Verify that is a probability density function.
(b)
What is the probability that a battery will have a life
span less than 10 months?
(c)
What is the probability that a battery will have a life
span more than 2 years?
(d)
What is the probability that a battery will have a life
span between 1.5 and 4 years?
(e)
Determine the mean value of the life span of the
batteries.
5. The probability density function of the successful
outcome from some experiment is given by the function below, where t is in minutes.
(a)
Verify that is a probability density function.
(b)
What is the probability of a successful outcome
happening in less than 12 minutes?
(c)
What is the probability of a successful outcome
happening after 25 minutes?
(d)
What is the probability of a successful outcome
happening between 10 and 75 minutes?
(e)
What is the mean time of a successful outcome from the
experiment?
6. Determine the value of c for which the function below will be a probability density
function.
7. Use the function below for this problem and assume a > 0.
(a)
Determine the value of c for which this function will be a probability density function.
(b)
Using the value of c
found in the first part determine the mean value of the probability density
function.