STAT311 Practice Questions II
Question 1
An urn contains 2 white ball and 3 red balls. Two balls are randomly drawn
from the urn with replacement. Let X be the number of red balls drawn, and let Y be the
draw on which the first red ball is drawn. (For example: the draw WR would give X = 1
and Y = 2.)
(a)
Give the joint probability (mass) function p
X
,
Y
(x
,
y) of X and
Y.
(b)
Give the probability (mass) function for X and Y: p
X
(x) and
p
Y
(y).
(c)
Find E(X
*
I
{
Y=2
}
).
(d)
Are X and Y are independent? (You must give a correct reason
for your answer.)
Question 2
Suppose that X is the number of prairie dogs found in a square mile of prairie,
and it has a Poisson(
μ
) distribution.
Suppose the probability that each day a young boy
captures a prairie dog at a certain place is
θ
, and Y is the number of days until the young
boy captures the first prairie dog. Find simple formulas in terms of
μ
and
θ
for the following
probabilities. (The formulas should not involve an infinite sum.)
(a)
P(XY
<
3).
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 Fall '08
 Staff
 Probability, Probability theory, Cumulative distribution function, Mr. Pickwick, ﬁrst prairie dog

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