The probability density function of the time to failure of an electronic component in a copier (in hours) is f(x)= e^-x/100 /1000. Determine the probability that

a. A component lasts more than 3000 hours before failure.

b. A component fails in the interval from 1000 to 2000 hours.

c. A component fails before 1000 hours

d. Determine the number of hours at which 10% of all components have failed.

e. Determine the cumulative distribution function for the distribution. Use the cumulative distribution function to determine the probability that a component lasts more than 3000 hours before failure.

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The fundamentals

A continuous random variable can take infinite values in the range associated function of that variable. Consider is a function of a continuous random variable within the range , then the total probability in the range of the function is defined as:

The probability of the function is always greater than 0. The cumulative distribution function is defined as:

The cumulative distribution function for the random variable X has the property,

The probability density function for the random variable X has the properties,

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