If the random variable X is exponentially distributed and the parameter of the distribution λ = 4,then P(X ≤ 1)= 0.25.

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JayLee Culpepper · Accepted Answer

Final Answer : False, Explanation :   For an exponentially distributed random variable X with rate parameter λ = 4, the probability that X is less than or equal to 1 is calculated using the formula   1 − e − λ x 1 - e^{-\lambda x} 1 − e − λ x  . Substituting λ = 4 and x = 1, we get   1 − e − 4 ∗ 1 = 1 − e − 4 1 - e^{-4*1} = 1 - e^{-4} 1 − e − 4 ∗ 1 = 1 − e − 4  , which is approximately 0.982, not 0.25.

If the random variable X is exponentially distributed and the parameter of the distribution λ = 4,then P(X ≤ 1)= 0.25.

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