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.

XX	3	4	5	6	7	8	9	10
P(X)P(X)	0.10.1	0.270.27	0.350.35	0.160.16	0.040.04	0.040.04	0.020.02	?

(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 is not a 10-room unit? P(X≠10)P(X≠10) =

(e) What is the probability that a unit chosen at random has three rooms? P(X=3)P(X=3) =

Answer 1

Given probability distribution table :

a)

Discrete random variable :

A discrete variable is a variable which can only take a countable number of values .

For example : 1) number of students present , 2 ) Number of car accidents in month etc.

Continuous random variable :

A continuous random variable is a random variable where the data can take infinitely many values.

For example : 1) Weight of people 2) Height of student in class etc.

In this example x takes 8 values ( 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 )

So , it is discrete random variable

b)

We know sum of all probabilities is 1

P( x=3 ) + P( x=4) + P( x=5 ) + P( x=6)+P( x=7 ) + P( x=8) + P( x=9 ) + P( x=10 ) = 1

0.1+ 0.27+ 0.35+0.16+0.04+0.04+0.02 + P( x=10 )

0.98 + P( x=10 ) = 1

P( x=10 ) = 1 - 0.98 = 0.02

c )

P( x > 5 ) = P( x=6)+P( x=7 ) + P( x=8) + P( x=9 ) + P( x=10 )

P( x > 5 ) = 0.16+0.04+0.04+0.02 + 0.02

P( x > 5 ) = 0.28

d )

P( x 10 ) = 1 - P( x = 10 ) = 1 - 0.02 = 0.98

e)

P(X=3) = 0.1