In a visual word recognition experiment, a participant has to recognize whether a string shown on

screen is a meaningful word $($e$.$g$.,$ "book"$)$ or a non$-$word $($e$.$g$.,"$bktr$").$ The participant is asked to

answer "yes" if the shown string is a meaningful word, and $"$no$"$ if it is a meaningless non$-$word.

Suppose a participant is shown $5$ strings on the screen one by one. The time taken by the participants to recognize each string is shown below $($in milliseconds$)$:

Recognition time for $5$ strings: $303,443,220,560,880$

Suppose the random variable X represents the string recognition times.

A researcher proposes a hypothesis that the string recognition times are generated by the probability density functions f$($x$,)$