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Let the random variable XX be the number of rooms in a randomly chosen owner-occ

ID: 3203643 • 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 between four and six rooms? P(4X6)P(4X6) =

(d) What is the probability that a unit chosen at random is not a 10-room unit? P(X10)P(X10) =

(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) 0.080.08 0.270.27 0.320.32 0.190.19 0.040.04 0.050.05 0.030.03 ?

Explanation / Answer

a. X is a DISCRETE random variable as it takes discrete values only.

b. P(X=10) = 1 - (0.08 + 0.27 + 0.32 + 0.19 + 0.04 + 0.05 + 0.03) = 0.02

As sum of all probabilities should be 1.

c. P(4 <= X <= 6) = P(X=4) + P(X=5) + P(X=6) = 0.27 + 0.32 + 0.19 = 0.78

d. P(X 10) = 1 - P(X=10) = 1 - 0.02 = 0.98

e. P(X=3) = 0.08