3. Let random variable X has exponential distribution with parameter ν.Find probabilityP (X ∈ [E(X) − σX ; E(X) + σX ])where σX is standard deviation of X.

Question

3. Let random variable X has exponential distribution with parameter ν.Find probabilityP (X ∈ [E(X) − σX ; E(X) + σX ])where σX is standard deviation of X.
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Solution 1

The exponential distribution is defined as:

f(x|ν) = νe^(-νx) for x >= 0, and 0 otherwise.

The expected value E(X) and the standard deviation σX for an exponential distribution are both equal to 1/ν.

So, we are looking for P(X ∈ [1/ν - 1/ν ; 1/ν + 1/ν]) = P(X ∈ [0 ; 2/ν]).

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