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Math 425 (Fall ’07)
Midterm 2
November 7, 2007
1 (10 pts)
i) Give an example of a discrete random variable and one of a continuous random variable.
ii) What is a random variable?
iii) Describe (brieﬂy) the role of the mean and the variance.
iv) What is the formula for the variance?
v) Assume
X
is the binomial distribution with parameters
n
= 100 and
p
= 0
.
005. How do
you suggest to compute
P
(
X
≤
2)?
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View Full Document2 (20 pts) For each of the random variables X below, determine the type of distribution which
best models X. Give the values of the parameters of the distribution chosen. Give the reasons
for your choice of the distribution and state your assumptions.
i) A fair coin is tossed until head appears for the ﬁfth time. X = total number of tosses
made.
ii) There are 100 ﬁsh in a pond, 20 of which are carp. Suppose that 30 ﬁsh are caught. X
= the number of carp.
iii) There are 1 million participants in a nationwide lottery. Every participant has a 1/500,000
chance of winning a milliondollar grand prize. X = the number of winners of the grand
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 Spring '10
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 Math, Variance

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