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

Calculus II - Practice Problems

1. Let,

 

(a)    Show that  is a probability density function.

(b)   Find .

(c)    Find .

(d)   Find .

(e)    Determine the mean value of X.

[Solution]

 

2. For a brand of light bulb the probability density function of the life span of the light bulb is given by the function below, where t is in months.

 

(a)    Verify that  is a probability density function.

(b)   What is the probability that a light bulb will have a life span less than 8 months?

(c)    What is the probability that a light bulb will have a life span more than 20 months?

(d)   What is the probability that a light bulb will have a life span between 14 and 30 months?

(e)    Determine the mean value of the life span of the light bulbs.

[Solution]

 

3. Determine the value of c for which the function below will be a probability density function.

 

[Solution]

 

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

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