Question

given the probability model in the table below, what is the expected value of the random variable? x 40 20 5 p(x) 0.15 0.3 0.55

Explanation:

Step1: Recall the formula for expected value

The formula for the expected value \( E(X) \) of a discrete random variable is \( E(X)=\sum_{i}x_{i}P(x_{i}) \).

Step2: Substitute the values into the formula

Here, \( x_1 = 40\), \(P(x_1)=0.15\); \(x_2 = 20\), \(P(x_2)=0.3\); \(x_3 = 5\), \(P(x_3)=0.55\).
So, \(E(X)=(40\times0.15)+(20\times0.3)+(5\times0.55)\).

Step3: Calculate each product

\(40\times0.15 = 6\); \(20\times0.3=6\); \(5\times0.55 = 2.75\).

Step4: Sum the products

\(E(X)=6 + 6+2.75=14.75\).

Answer:

\(14.75\)