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. Find (a) $E[X]$, (b) $\operatorname{Var}(X)$.
Added by Brian G.
Step 1
Step 1: Calculate $E[X]$ using the formula $E[X] = \lambda \cdot E[T]$, where $\lambda$ is the rate of the Poisson process and $E[T]$ is the expected time between train arrivals. Show more…
Show all steps
Your feedback will help us improve your experience
Satyam Gupta and 100 other Probability educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Recommended Videos
thought
Ameer S.
The number of customers arriving per hour at a certain automobile service facility is assumed to follow a Poisson distribution with mean $\lambda=7$. (a) Compute the probability that more than 10 customers will arrive in a 2 -hour period. (b) What is the mean number of arrivals during a 2-hour period?
Ajiboye T.
There is one hospital at the northern end of a particular county and another hospital at the southern end of the county. Suppose that arrivals to each hospital's emergency room occur according to a Poisson process with the same rate $\lambda$ and that the two arrival processes are independent of one another. Starting at time $t=0,$ let $Y$ be the elapsed time until at least one arrival has occurred at each of the two emergency rooms. Determine the probability distribution of $Y$ .
Random Processes
Poisson Processes
Recommended Textbooks
Probability with Applications in Engineering, Science, and Technology
Probability and Statistics for Engineers and Scientists
Applied Statistics and Probability for Engineers
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD