Probability Question - Exponential Distribution

[GreenPrint]

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?

 

[Ray Vickson]

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?

Yes. You are missing the facts that μ-σ = 0 and μ+σ = 2μ, so you want P(0 ≤ X ≤ 2μ). Why would you suppose that is 0?

 

[GreenPrint]

oh thanks i missed that