exercise:Cf1b53da02: Difference between revisions
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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> Let <math>X</math> be a random variable which is Poisson distributed with parameter <math>\lambda</math>. Show that <math>E(X) = \lambda</math>. '' Hint'': Recall that <math display="block"> e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \cd...") |
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Let <math>X</math> be a random variable which is Poisson distributed with parameter <math>\lambda</math>. Show that <math>E(X) = \lambda</math>. '' Hint'': | |||
Poisson distributed with parameter <math>\lambda</math>. Show that <math>E(X) = \lambda</math>. '' Hint'': | |||
Recall that | Recall that | ||
Latest revision as of 17:35, 14 June 2024
Let [math]X[/math] be a random variable which is Poisson distributed with parameter [math]\lambda[/math]. Show that [math]E(X) = \lambda[/math]. Hint: Recall that
[[math]]
e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \cdots\,.
[[/math]]