Learn / Library / Statistics

Block trades over a pair of sessions

StatisticsEasy

A venue prints $6$ block trades in a $4$ hour session and $9$ block trades in a $16$ hour session. Both counts are independent and Poisson, with the same rate $λ$ per hour. What is the maximum likelihood estimate of $λ$ ? Give a fraction.

Checking an answer needs JavaScript. The hint and the solution open without it.

Hint

Write the log likelihood of both counts and set its slope to zero.

Solution

The log likelihood is $15 log λ - 20 λ$ , up to terms without $λ$ .
Its slope $15/ λ - 20$ is zero at $λ = \frac{15}{20}$ .
So the estimate is $λ^= \frac{3}{4}$ .

Answer: $\frac{3}{4}$

Next question Back to the library