Question

The length of life of an electronic component has an exponential probability density function with mean 1000 hours. Find the probability that a component lasts at least 1500 hours

Answer 1

The probability that a component lasts at least 1500 hours using the exponential probability density function is 0.22313016014843.

The formula used to define the exponential distribution is called the exponential distribution formula. The variable needs to be continuous and independent for an exponential distribution. You may find the exponential distribution formula by using:

$f(x) = me^{-mx} \text{ or } f(x) = (1/\mu) e^{-(1/\mu)x}$

Where m is the rate parameter or the decay parameter, and μ is the mean.

In the question, the mean, μ = 1000 hours, and the variable, x = 1500 hours.

But, we need to find the probability that the component lasts at least 1500 hours, that is, x is greater than or equal to 1500, that is, f(x ≥ 1500), which, using the calculator, is computed to be 0.22313016014843.

Thus, the probability that a component lasts at least 1500 hours using the exponential probability density function is 0.22313016014843.

Learn more about the exponential probability density function at

brainly.com/question/13339415

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