Question

using the data from the table, what is p(3)?
what is the mean of the probability distribution?

Explanation:

Step1: Recall the formula for the mean of a probability distribution

The mean \(\mu\) of a probability distribution is given by \(\mu=\sum_{i}x_{i}P(x_{i})\)

Step2: Calculate each term \(x_{i}P(x_{i})\)

• For \(x = 0\): \(0\times0.1=0\)
• For \(x = 1\): \(1\times0.2 = 0.2\)
• For \(x = 2\): \(2\times0.4=0.8\)
• For \(x = 3\): \(3\times0.2 = 0.6\)
• For \(x = 4\): \(4\times0.1=0.4\)

Step3: Sum up the terms

\(\mu=0 + 0.2+0.8 + 0.6+0.4\)
\(\mu=2.0\)

Answer:

The mean of the probability distribution is \(2.0\)