Unformatted text preview: Example 2:
The average lifetime of a certain type of light bulb is 500 hours. Assume that if the current light
bulb burns out, it will get changed immediately. Please answer the following questions.
a) Name the distribution and parameter(s) of the light bulb's life.
X - Expl/ =SUO or A = sto )
X = Lightbulb life in how's
b) What's the probability that a light bulb lasts more than 520 hours?
: Tail Probability:
e sto . Sto
c) If we know a light bulb is still working after 230 hours, what's the probability that it
burns out before reaching 600 hours.
P(x 4100 1 x > 230)
: memoryless :
P(X460b-230) = P(X 2370) = F. (370) - 1- e 520 50- 0.5229
d) What is the average number of light bulbs that will be used in 2000 hours?
Y= Hof lightwlbs used in ?it hours
Y~ Poisson (At = Soo . 2000 = 4)
e) What is the probability that there are between 4 and 6 light bulbs (inclusive) used in 2000
=P(Y=4)+ P(Y=s) +P(Yl )
f) If we know that there were 6 light bulbs used in 2000 hours, what's the probability that 2
were used in the last 400 hours?
N=H of Wuvs used in the last 40D hows
In the First
Nw Bin (n=b, P = yard
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- Fall '09
- Incandescent light bulb