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

D. 0.1353

B. 0.0473

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