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For a certain experiment, the Poisson distribution with parameter <math>\lambda = m</math> has been assigned. Show that a most probable outcome for the experiment is the integer value <math>k</math> such that <math>m - 1 \leq k \leq m</math>. Under what | |||
parameter <math>\lambda = m</math> has been assigned. Show that a most probable outcome for the | |||
experiment is the integer value <math>k</math> such that <math>m - 1 \leq k \leq m</math>. Under what | |||
conditions will there be two most probable values? '' Hint'': Consider the ratio | conditions will there be two most probable values? '' Hint'': Consider the ratio | ||
of successive probabilities. | of successive probabilities. | ||
Latest revision as of 00:09, 14 June 2024
For a certain experiment, the Poisson distribution with parameter [math]\lambda = m[/math] has been assigned. Show that a most probable outcome for the experiment is the integer value [math]k[/math] such that [math]m - 1 \leq k \leq m[/math]. Under what conditions will there be two most probable values? Hint: Consider the ratio of successive probabilities.