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Calculus II - Assignment Problems
 Integration Techniques Previous Chapter Next Chapter Parametric Equations and Polar Coordinates Hydrostatic Pressure Previous Section

## 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.

 Hydrostatic Pressure Previous Section Integration Techniques Previous Chapter Next Chapter Parametric Equations and Polar Coordinates

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