X∈Γ(λ) (exponential random variable).We have λ=20. So (i) mean of X M(X)=λ1=201.(ii) First we find the distribution function of X F(x).F(x)=∫−∞xf(t)dt∫0x20e−20tdt=(20⋅(−201)e−20t)0x=1−e−20xF(x)=1−e−20x, x>0F(x)=0, otherwise.P(X<1000)=F(1000)=1−e−20⋅1000≈1.(iii)P(X>3000)=1−P(X≤3000)=1−(1−e20⋅3000)≈0.
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