The number of hours between successive train arrivals at the station is uniformly distributed on (0, 1). passengers arrive according to a poisson process with rate 7 per hour. suppose a train has just left the station. let x denote the number of people who get on the next train. what are the e[x] and var[x]?

The value of .

The value of .

Step-by-step explanation:

Consider the provided information.

The number of hours between successive train arrivals at the station is uniformly distributed on (0, 1). Passengers arrive according to a Poisson process with rate 7 per hour.

Let X denote the number of people who get on the next train.

Part (A)

Here, X = N(T), N(t) ∼ Poisson(λt),  and λ = 7

Therefore, E(N(T)|T) = λT

Now find E(X) as shown below

Hence, the value of .

Part (B)

Now we need to find VAR[X]

Hence, the value of

the answer is (-4,-4)

hope this ! : d