Consider an experiment where three lightbulbs with independe

Consider an experiment where three lightbulbs with independent lifetimes are turned on simultaneously, each one having a lifetime that is uniformly distributed between 1 and 3 years. Find the PDF and expected value of the time to last one burning out.

Solution

PDF FOR THE 3 BULB FOR TIME BEING FROM 1 TO 3

1 BULB SUSTAIN THE TIMELINE = 1/3

2BULP SUSTAIN THE TIME LINE = 2/3

3 BULB SUSTAIN THE TIME LINE = 3/3

NOW EXPECTATION = E(X)= X*P(X)+X*(P(X))+....

= 1*1/3+2*2/3+3/3/3=14/3