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.

Check the explanation

Step-by-step explanation:

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,

Kindly check the attached image below to see the full explanation to the question above.

1)is not similar since corresponding sides are not in the same ratio

2)are similar since corresponding sides are in the same ratio and corresponding angles are equal

hope it will

#faazmessi