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Statistics / Mr. Hansen |
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Name:
__________________________________ |
Test
on Chapters 7 and 8
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Instructions and Scoring.
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1.(a) |
Using words, symbols, or a
combination of the two, explain how to compute the expected value of a
discrete random variable. |
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(b) |
Let X be a discrete random variable such that P(X = 7) = .5 and P(X
= 11) = .5. Compute the standard deviation of X. Work is not required, but write your answer as an equation
using correct notation. |
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2.(a) |
Compute the mean of random
variable X in #1(b). Show your
work. |
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(b) |
Using the definition of
s.d., explain why your answer to #1(b) is logical. Or, if you cannot remember
the verbal definition, compute #1(b) a second time, this time showing all
work in full detail. |
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3. |
Random variables W and Y are independent, with means of –3 and 14, respectively, and
standard deviations of 2.2 and 3.3, respectively. If each is normally
distributed, compute |
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(a) |
E(W – Y) |
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(b) |
Var(W – Y) |
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(c) |
Var(3W – 7) |
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Show work for full credit. |
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4. |
American 18-year-old males
have heights that follow N(70,
2.9), while American 17-year-old males have heights that follow N(69.3, 3.2). Show your work and
compute |
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(a) |
the expected height
difference between a randomly selected 18-year-old and a randomly selected
17-year-old (both American males); |
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(b) |
the probability that the
18-year-old is taller. |
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5,6.(a) |
State the full
definition/description of a geometric random variable. |
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(b) |
State the full
definition/description of a binomial random variable. |
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(c) |
Give an example of a
geometric random variable with sufficient description to guarantee that it
really is geometric. |
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(d) |
Repeat (c) for binomial. |
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7.(a) |
One lottery ticket in every
100 is a winner in a new scratch-off game. If I buy 500 tickets, are these
independent trials? If yes, how do you know? If not, are they “close enough”
to independent? How do you know? |
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(b) |
Compute the expected # of
winners I have, and the s.d. of the number of winners. Show work. |
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8.(a) |
In #7, compute the
probability that I have fewer than 5 but at least 3 winners. Show work. |
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(b) |
Compute the probability
that I do not find a winner before the 120th ticket. Show work. |