What is the probability that x is less than 5, given the function below? f(x) = (1/10) e^-^x^/10 x 0 A) 0.6065 B) 0.0606 C) 0.3935 D) 0.9393

Question

Quizplus · Accepted Answer

We need to find the probability that x is less than 5, which can be written as P(x < 5). Using the given function, we can find the cumulative distribution function (CDF) as follows: F(x) = ∫f(t) dt from -∞ to x = (1/10) ∫e^(^-^{t) (1/10}) dt from -∞ to x = (-1/10) e^(^-^{t) from -∞ to x
= (-1/10}) (e^(^-^{x) - e^(-∞))
= (-1/10}) (e^(^-^{x))

Now, we can use the CDF to find the required probability:

P(x < 5) = F(5)
= (-1/10}) (e^(^-^{5))
≈ 0.3935

Therefore, the best choice is C.}

What Is the Probability That X Is Less Than 5