Lifetime of a light bulb follows exponential distribution with $x$ means hours. If $n$ bulbs were switched on at same time and after $t$ time only $n-m$ were found to be functioning. Remaining $m$ bulbs had lifetime $x_{i}$ for $i=1$ to $m$. What will be the PDF of the bulbs that are still functioning?

My confusion is, since these $n-m$ bulbs are still functioning how can we find their PDF?

  • $\begingroup$ Presumably the individual lightbulbs at the start have identical and independent distributions. It may be worth remembering that exponential distributions have the memorylessness property $\endgroup$
    – Henry
    Feb 19, 2022 at 9:13
  • $\begingroup$ The question doesn't make sense - if "only $n-m$ were found to be functioning," why would there be a "remaining $m$ bulbs?" $\endgroup$
    – Math1000
    Mar 6, 2022 at 13:26


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