Paul's Online Math Notes
Calculus II (Assignment Problems) / Applications of Integrals / Probability   [Notes] [Practice Problems] [Assignment Problems]

Calculus II - Assignment Problems

 Probability

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.

 


Calculus II (Assignment Problems) / Applications of Integrals / Probability    [Notes] [Practice Problems] [Assignment Problems]

© 2003 - 2017 Paul Dawkins