Let the random variable XX be the number of rooms in a randomly chosen owner-occ
ID: 3074512 • Letter: L
Question
Let the random variable XX be the number of rooms in a randomly chosen owner-occupied housing unit in a certain city. The distribution for the units is given below.
(a) Is XX a discrete or continuous random variable? (Type: DISCRETE or CONTINUOUS)
ANSWER:
(b) What must be the probability of choosing a unit with 10 rooms? P(X=10)P(X=10) =
(c) What is the probability that a unit chosen at random has more than 5 rooms? P(X>5)P(X>5) =
(d) What is the probability that a unit chosen at random has less than five rooms? P(X<5)P(X<5) =
(e) What is the probability that a unit chosen at random has three rooms? P(X=3)P(X=3) =
XX 3 4 5 6 7 8 9 10 P(X)P(X) 0.090.09 0.260.26 0.360.36 0.160.16 0.040.04 0.040.04 0.030.03 ?Explanation / Answer
a) X is a discrete random variable.
b) P(X = 10) = 1 - (0.09 + 0.26 + 0.36 + 0.16 + 0.04 + 0.04 + 0.03)
=1 - 0.98 = 0.02
c) P(X > 5) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)
= 0.16 + 0.04 + 0.04 + 0.03 + 0.02 = 0.29
d) P(X < 5) = P(X = 3) + P(X = 4)
= 0.09 + 0.26 = 0.35
e) P(X = 3) = 0.09
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