Question

find the expected value of the random variable.
what is the expected value? (type an integer or a decimal.)

Explanation:

Step1: Recall the formula for expected value

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

Step2: Calculate each term

For \(x = 2\) and \(P(x)=0.3\), the term is \(2\times0.3 = 0.6\)
For \(x = 3\) and \(P(x)=0.1\), the term is \(3\times0.1=0.3\)
For \(x = 4\) and \(P(x)=0.2\), the term is \(4\times0.2 = 0.8\)
For \(x = 5\) and \(P(x)=0.4\), the term is \(5\times0.4=2\)

Step3: Sum up the terms

\(E(X)=0.6 + 0.3+0.8 + 2\)
\(E(X)=3.7\)

Answer:

\(3.7\)