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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.

Let the random variable x be the number of rooms in a randomly chosen owner- occupied-example-1

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5 votes

(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

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