# Thread:

1. ## Expected time from Poisson process

Hi,

Let's say I have cars passing a point as a Poisson process with having stationary flow of 100 cars/hr. How would I go about finding the expected amount of time needed to observe one headway (time between cars) larger than three times the mean headway?

Thanks!

2. Arrivals in a Poisson process are $\exp(\lambda)$. Now what is the expected time between cars? Easy, $\frac{1}{\lambda}$. State your question in terms of an exponential distribution (i.e. what is the prob. that an arrival takes longer than 3 times the mean), then it should be pretty clear what the answer is.

Good luck.
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9515901803970337, "perplexity_flag": "middle"}