Question

The number of minutes between successive bus arrivals at Mehmet's bus stop is exponentially distributed with unknown parameter .

Mehmet's prior information regarding  (real valued, i.e., a continuous random variable) can be summarized as a continuous uniform PDF in the range from 0 to 0.63.

Mehmet has recorded his bus waiting times for four days. These are 12, 8, 26 and 23 minutes. Assume that Mehmet's bus waiting times in different days are independent.

Compute the MAP (maximum a posteriori probability) rule based estimate for  given the data collected by Mehmet.

Round your answer to five decimal digits after the decimal point.

Answer 1