Question

the table below shows the probability distribution of a random variable x.
what is the expected value of x?
write your answer as a decimal.

Explanation:

Step1: Recall the formula for expected value

The formula for the expected value \(E(X)\) of a discrete random variable is \(E(X)=\sum_{i}x_{i}P(x_{i})\), where \(x_{i}\) are the values of the random variable and \(P(x_{i})\) are their corresponding probabilities.

Step2: Substitute the values into the formula

For \(x_1 = 10\) and \(P(x_1)=0.5\), \(x_1P(x_1)=10\times0.5 = 5\).
For \(x_2 = 11\) and \(P(x_2)=0.4\), \(x_2P(x_2)=11\times0.4=4.4\).
For \(x_3 = 12\) and \(P(x_3)=0.1\), \(x_3P(x_3)=12\times0.1 = 1.2\).

Step3: Sum up the products

\(E(X)=5 + 4.4+1.2\)

Answer:

\(10.6\)