Probability

Question

Comments

Can you post a clearer picture

Answer 1

var(X) in exponential distribution is 1/(parameter)² i.e 1/λ² here so option B

var(3X+5)

⇒3var(X) + var(5)

⇒3*1/λ² + 0                    as var(constant)=0;var(X)=1/λ²

⇒3/λ²

^{so option B}

Comments

can you please explain the first question how it is (1/(parameter)^2)?

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now you can evaluate the integral to arrive at desired result.you can find this proof in any standard book for variance the formula is var(X) =E[x²]-(E[x])²

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var[3x+5]=var[3x]+var[5]
=3^2var[x]+0
= 9/λ^{2
I think this should be answer.}