Answer:
D. 0.1353
B. 0.0473
Step-by-step explanation:
For an exponentially distributed random variable, the cumulative distribution function is:
[tex]P(x\leq a) = 1 - e^{-\lambda a}\\P(x\geq a) = e^{-\lambda a}[/tex]
with parameter λ=2, then P(X≥1) is equal to:
[tex]P(x\geq 1) = e^{-2*1}=0.1353[/tex]
D. 0.1353
with parameter λ=1.5, then P(2≤X≤4) is equal to
[tex]P(2\leq x \leq 4) = P(x \leq 4) - P(x\leq 2)\\P(2\leq x \leq 4) =1 - (e^{-1.5*4}) - (1-(e^{-1.5*2}))\\P(2\leq x \leq 4) = 0.0473[/tex]
B. 0.0473
