Question

1. determine whether the random variable is discrete or continuous. in each case, state the possible values of the random variable.

a. the number of customers arriving at a bank between noon and 1:00 p.m.
b. the time it takes for a light bulb to burn out.

1. what are the two requirements for a discrete probability distribution?
2. determine whether the distribution is discrete probability distribution.
3. determine the required value of the missing probability to make the distribution a discrete probability distribution.

Explanation:

Step1: Recall the property of discrete probability distribution

The sum of all probabilities \(P(x)\) in a discrete probability distribution is \(1\). Let the missing probability for \(x = 4\) be \(p\). Then we have the equation \(0.17+p + 0.44+0.13=1\).

Step2: Simplify the left - hand side of the equation

First, add the known probabilities: \(0.17+0.44 + 0.13=0.74\). So the equation becomes \(0.74 + p=1\).

Step3: Solve for \(p\)

Subtract \(0.74\) from both sides of the equation: \(p=1 - 0.74\).

Answer:

\(p = 0.26\)