The lifetime of a component is exponentially distributed with parameter 2. The probability that its

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Question

The lifetime of a component is exponentially distributed with parameter 2. The probability that its lifetime exceeds the expected lifetime (rounded to 2 decimal places) is ________.

Accepted Answer

Answer: 0.37 (accepted range 0.35 to 0.39 per official key)Concept -- Exponential Distribution: For an exponential distribution with rate parameter lambda = 2, the probability density function is f(x) = 2*e^(-2x) for x >= 0. The expected value (mean) is E[X] = 1/lambda = 1/2.We need P(X > E[X]) = P(X > 1/2). Using the survival function of the exponential distribution: P(X > t) = e^(-lambda * t). So P(X > 1/2) = e^(-2 * 1/2) = e^(-1) approximately 0.3679.Rounded to 2 decimal places: 0.37. This result holds for any exponential distribution: the probability of exceeding the mean is always e^(-1) regardless of the rate parameter.

The lifetime of a component is exponentially distributed with parameter 2. The probability that its lifetime exceeds the expected lifetime (rounded to 2 decimal places) is ________.

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The lifetime of a component is exponentially distributed with parameter 2. The probability that its lifetime exceeds the expected lifetime (rounded to 2 decimal places) is ________.

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