Suppose that x has an exponential distribution with $\theta = 1.5 \text {. Find } P ( x 1 )$
A) 0.513417
B) 0.223130
C) 0.486583
D) 0.776870

Question

Suppose that x has an exponential distribution with $\theta = 1.5 \text {. Find } P ( x > 1 )$
A) 0.513417
B) 0.223130
C) 0.486583
D) 0.776870

Quizplus · Accepted Answer

The probability density function of the exponential distribution is given by:$$f(x) = \theta e^{-\theta x}$$where $\theta$ is the rate parameter.In this case, $\theta = 1.5$, so the probability density function is:$$f(x) = 1.5 e^{-1.5 x}$$The probability that $x > 1$ is given by the integral of the probability density function from $1$ to infinity:$$P(x > 1) = \int_1^\infty 1.5 e^{-1.5 x} dx$$This integral evaluates to:$$P(x > 1) = 0.513417$$Therefore, the correct answer is A.

Suppose That X Has an Exponential Distribution With θ=1.5. Find P(x>1)\theta = 1.5 \text {. Find } P ( x > 1 )θ=1.5. Find P(x>1)

Suppose That X Has an Exponential Distribution With $\theta = 1.5 \text {. Find } P ( x > 1 )$