Question

Let the random variable x 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.

Answer 1

(a)

Since X can only assume whole values, it is a discrete random variable.

(b)

The sum of all probabilities in the table must be equal to 1, so we have:

$\begin{gathered} 0.07+0.22+0.41+0.2+0.05+0.03+0.01+P(10)=1\\ \\ 0.99+P(10)=1\\ \\ P(10)=1-0.99\\ \\ P(10)=0.01 \end{gathered}$

(c)

The values of x smaller than 5 in the table are 3 and 4, so we have:

$P(X<5)=P(3)+P(4)=0.07+0.22=0.29$

(d)

For x between 4 and 6, we have:

$P(4\leq x\leq6)=P(4)+P(5)+P(6)=0.22+0.41+0.2=0.83$

(e)

Looking at the table, for x = 3 we have:

$P(3)=0.07$