The useful life of an electrical component is exponentially...

The useful life of an electrical component is exponentially distributed with a mean of 1,000 hours. a. What is the probability the circuit will last more than 2,000 hours? b. What is the probability the circuit will last between 1,000 and 1,250 hours? c. What is the probability the circuit will fail within the first 0 hours?

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00:01 Hi, i'm david and i'm here to help you answer your question.

00:04 Now let me bring up your question here.

00:07 In this question we want to review about the exponential distribution.

00:11 Let me remind you that it will the x followed by exponential when the mean equal to petal and then the density of the x it will equal to 1 over petal each the power minus x over beta for the x greater than 0.

00:27 Here we have the x here it will equal to the life of the electrical component.

00:37 So it will follow by exponential, with the mean it will equal to 1 ,000 hours.

00:44 And then we will get the density of the x, it will equal to 1 over 1 ,000, e to the power minus x over 1 ,000 for the x greater than 0.

00:56 In the question, i want to find the probability that the life it will be more than 2 ,000 hours.

01:06 So actually, quite it than 2 ,000.

01:08 Now to find this probability, it could be much easier to do with the integral from 2000 to the infinity.

01:19 And then we have density will be 1 over 1 ,000, each the power minus x over 1 ,000.

01:27 The x.

01:28 Untie derivative of this one equal to minus e to the power minus x over 1000, evaluate from 2000 to infinity.

01:38 It will put the infinity inside.

01:40 We got the zero...

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