3) A light fixture contains five lightbulbs. The lifetime of each bulb is exponentially distributed with mean 200 hours. Whenever a bulb burns out, it is replaced. Let T be the time of the first bulb...

3) A light fixture contains five lightbulbs. The lifetime of each bulb is exponentially distributed with mean 200 hours. Whenever a bulb burns out, it is replaced. Let T be the time of the first bulb replacement. Let Xi, i = 1, . . . , 5, be the lifetimes of the five bulbs. Assume the lifetimes

of the bulbs are independent.

e) Find P T < 100<br>f) Does T have an exponential distribution?<br>g) Find the mean of T'.<br>h) If there were n light bulbs, and the lifetime of each was exponentially distributed with<br>parameter A, what would be the distribution of T?<br>

Extracted text: e) Find P T < 100="" f)="" does="" t="" have="" an="" exponential="" distribution?="" g)="" find="" the="" mean="" of="" t'.="" h)="" if="" there="" were="" n="" light="" bulbs,="" and="" the="" lifetime="" of="" each="" was="" exponentially="" distributed="" with="" parameter="" a,="" what="" would="" be="" the="" distribution="" of="">

Jun 07, 2022

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3) A light fixture contains five lightbulbs. The lifetime of each bulb is exponentially distributed with mean 200 hours. Whenever a bulb burns out, it is replaced. Let T be the time of the first bulb...

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