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Unformatted text preview: 1. Suppose that the three inspectors at a ﬁlm factory are supposed
to stamp the expiration data on each package of ﬁlm at the end of
assembly line. John , who stamps 25% of the packages, fails to stamp
the expiration date once in every 200 packages, Tom , who stamps
60% of the packages, fails to stamp the expiration date once in every
100 packages, Jeﬀ, who stamps 15% of the packages, fails to stamp the
expiration date once in every 90 packages. If a customer complains that
her package does not show the expiration date, what is the probability
that was inspected by John?
2.Ten people are randomly seated at round table. What is the probability that a particular couple will seat next to each other?
3. The life span in hours of an electrical component is a random
variable with cumulative distribution function
1 − e−x/50 x > 0
F (x) =
a. Find and sketch the pdf of X .
b. Find the standard deviation of X .
4. Suppose the random variables X and Y are jointly distributed
according to the pdf
fX,Y (x, y ) = (x2 + y 2 ), 0 < x < 1, 0 < y < 1
a) fX (x)
b) P (X < Y )
c) P (Y < 1/2|X = 1/2)
5. Suppose that the random variable X has moment generating
MX (t) =
1 − (1 − 0.25t)et
a. Find variance using moment generating function.
b. Find P (2 < X ≤ 4).
6. The driver of a truck loaded with 900 boxes of books will be ﬁned if
the total weight of the boxes exceeds 36450 pounds. If the distribution
of the weight of a box has a mean of 40 pounds and a variance of 36,
ﬁnd the approximate probability that the driver will not be ﬁned. 1 ...
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