The probability density function of the time to failure of an electronic component in a copier (in hours) is f(x) for 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.

The question is incomplete. Here is the complete question.

The probability density function of the time to failure of an electronic component in a copier (in hours) is

for x > 0. Determine the probability that

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

b. A componenet 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.

a. P(x>3000) = 0.5

              b. P(1000<x<2000) = 0.2325

              c. P(x<1000) = 0.6321

              d. 105.4 hours

Step-by-step explanation: Probability Density Function is a function defining the probability of an outcome for a discrete random variable and is mathematically defined as the derivative of the distribution function.

So, probability function is given by:

P(a<x<b) =

Then, for the electronic component, probability will be:

P(a<x<b) =

P(a<x<b) =

P(a<x<b) =

a. For a component to last more than 3000 hours:

P(3000<x<∞) =

Exponential equation to the infinity tends to zero, so:

P(3000<x<∞) =

P(3000<x<∞) = 0.05

There is a probability of 5% of a component to last more than 3000 hours.

b. Probability between 1000 and 2000 hours:

P(1000<x<2000) =

P(1000<x<2000) =

P(1000<x<2000) = 0.2325

There is a probability of 23.25% of failure in that interval.

c. Probability of failing between 0 and 1000 hours:

P(0<x<1000) =

P(0<x<1000) =

P(0<x<1000) = 0.6321

There is a probability of 63.21% of failing before 1000 hours.

d. P(x) =

0.1 =

-x = -1000.ln(0.9)

x = 105.4

10% of the components will have failed at 105.4 hours.

step-by-step explanation:

your mom

can you rephrase the question ? it is unclear : -)

step-by-step explanation: