Paul Meyer wrote:
Btw, in a stastics class I learned that light bulbs don't fail because of
filament
failure at switch-on. The failure rate is constant with time (I forget which
distribution
models this, but whichever is a "memoryless" distribution) which indicates that
the cause for failure is most likely external, i.e. power surges on the line.
P.S.
There is only one continuous random variable with the memoryless
property: the exponential random variable. (For discrete random
variables, the only one is the geometric random variable.)
The exponential random variable X can take on any number whatsoever that
is non-negative, i.e., 0 or positive. The probability density function
for X is f(x) = q*exp(-q*x) where q is the inverse of the expected value
of X: E[X] = 1/q. The variance of X is 1/q^2.
The probability density function f(x) means that the probability that
the random variable X is between a lower value x1 and a higher value x2
equals the area bounded by three sides of a rectangle plus a curved line
for the fourth side: the three straight sides have length f(x1), f(x2),
and x2-x1; the curved side is f(x) for x between the values x1 and x2.
To say this simpler, it is the area "underneath f(x) between x1 and x2."
I will caution that applying this pdf to the bulb burnout is an act of
faith: bulbs usually burn out when they are switched on (my previous
message). In any case, the "experiment" of bulb burn-out depends on the
conditions: are they run continuously until they burn out, or are they
subjected to vibrations during use or disuse, or are they switched on
and off frequently, etc.? It is not at all clear that the exponential
random variable will adequately model they empirical data of bulb
burn-out for all the experiments.
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