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ECO220Y: Homework, Lectures 13 & 14
Readings:
Section 7.4
Exercises:
7.92, 7.94, 7.96, 7.97, 7.98 (Note: Solve these Exercises without
a computer and without
using any
tables in the appendices)
Problems:
(1)
What two factors affect the probability of any particular number of successes in a Binomial experiment? For
example, what would affect the P(X = 1)?
Make sure to explain the intuition.
(2)
Would the following be good examples of a Binomial random variable: number of hearts drawn in 5 draws
with replacement from a standard 52 card deck; number of hearts drawn in 5 draws with
out
replacement from a
standard 52 card deck?
(3)
For which (finite) number of tosses of a fair coin is the probability of getting exactly 50% heads the biggest?
[Hint: Your answer should be of the form: n = #, where # is a number.] Explain and show work.
(4)
Consider doing a Binomial Experiment and defining a new random variable Y as the fraction
of successes
in the n trials.
For example, if there are 3 successes in 5 trials, Y would be 0.60 whereas the Binomial random
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 Spring '11
 tanaka
 Probability theory, Discrete probability distribution, binomial random variable

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