The discussion centers on calculating the probability for a random variable X with an exponential distribution and mean μ, specifically P(μ-σ≤X≤μ+σ). It is established that the standard deviation σ of an exponential distribution equals its mean μ. Therefore, the bounds for the probability calculation simplify to P(0 ≤ X ≤ 2μ). The conclusion is that the probability is not zero, as the range encompasses a significant portion of the distribution.
PREREQUISITESStudents studying probability theory, statisticians, and professionals in data analysis who require a solid understanding of exponential distributions and their properties.
GreenPrint said:Homework Statement
Suppose that X has an exponential distribution with mean μ. Find the probability that x lies within one standard deviation of its mean, that is find P(μ-σ≤X≤μ+σ)
Homework Equations
The Attempt at a Solution
If I'm not mistaken the standard deviation is equal to the mean of an exponential distribution so isn't the answer just zero or am I missing something important here?