Question

If a random variable X is exponentially distributed with parameter λ=2, then P(X≥1) is equal to

A. 0.3935
B. 0.8647
C. 0.6065
D. 0.1353

If a random variable X is exponentially distributed with parameter λ=1.5, then P(2≤X≤4) is equal to

A. 0.9527
B. 0.0473
C. 0.6617
D. 0.3383

Answer 1

Answer:

D. 0.1353

B. 0.0473

Step-by-step explanation:

For an exponentially distributed random variable, the cumulative distribution function is:

$P(x\leq a) = 1 - e^{-\lambda a}\\P(x\geq a) = e^{-\lambda a}$

with parameter λ=2, then P(X≥1) is equal to:

$P(x\geq 1) = e^{-2*1}=0.1353$

D. 0.1353

with parameter λ=1.5, then P(2≤X≤4) is equal to

$P(2\leq x \leq 4) = P(x \leq 4) - P(x\leq 2)\\P(2\leq x \leq 4) =1 - (e^{-1.5*4}) - (1-(e^{-1.5*2}))\\P(2\leq x \leq 4) = 0.0473$

B. 0.0473