Probability Question - Exponential Distribution

AI Thread Summary
The discussion revolves around calculating the probability that a random variable X, which follows an exponential distribution with mean μ, lies within one standard deviation of its mean. It is clarified that the standard deviation of an exponential distribution is equal to its mean, leading to the bounds μ-σ = 0 and μ+σ = 2μ. The correct probability to find is P(0 ≤ X ≤ 2μ), rather than assuming it to be zero. The initial misunderstanding is addressed, emphasizing the importance of correctly identifying the bounds for the probability calculation. This highlights the need for careful interpretation of statistical properties in exponential distributions.
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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?
 
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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?

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?
 
oh thanks i missed that
 

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