Question

Suppose that the buses arrive are scheduled to arrive at a bus stop at noon are always X minutes late, where X is an exponential random variable

Answer 1

Answer:

$e^{-5\lambda}$

Step-by-step explanation:

Looking at other sources :- Complete Question:

Suppose that the buses arrive are scheduled to arrive at a bus stop at noon are always X minutes late, where X is an exponential random variable with probability density function $f_X(x)=\lambda e^{-\lambda x} , x \geq 0$ Suppose you arrive at the bus stop precisely at noon . Find the probability that you have to wait for more than 5 min for the bus to arrive

.

1)  We need to find

$P(x\geq 5)=\int\limits^{\infty}_5 {f_X(x)} \, dx \\ \\=\int\limits^{\infty}_5 {\lambda e^{-\lambda x} } \, dx \\ \\ =\bigg\rvert_5^\infty \frac{\lambda e^{-\lambda x}}{-\lambda} \\ \\ = \bigg\rvert_5^\infty -e^{-\lambda x}\\ \\= e^{-5\lambda}$

Above answer is our required probability.

Answer 2

Step-by-step explanation:

e

−5λ

Step-by-step explanation:

Looking at other sources :- Complete Question:

Suppose that the buses arrive are scheduled to arrive at a bus stop at noon are always X minutes late, where X is an exponential random variable with probability density function f_X(x)=\lambda e^{-\lambda x} , x \geq 0f

X

(x)=λe

−λx

,x≥0 Suppose you arrive at the bus stop precisely at noon . Find the probability that you have to wait for more than 5 min for the bus to arrive

.