Question

please help The table below shows the probability distribution of a random variable Y. What is the expected value of Y? Write your answer as a decimal.

Answer 1

Step 1. We are given a table with values for Y and their corresponding probability P(Y).

Required: Find the expected value of Y.

Step 2. First, we will label the Y values as Y1, Y2, Y3, Y4 as shown in the diagram:

And we will label the corresponding probabilities as P1, P2, P3, and P4, shown in the following diagram:

Step 3. The formula to calculate the expected value E(Y) is:

$E(Y)=Y_1P_1+Y_2P_2+Y_3P_3+Y_4P_4$

Step 4. Substituting the values from step 2 into the formula from step 3:

$E(Y)=(14)(0)+(15)(0.6)+(16)(0.3)+(17)(0.1)$

Solving the operations:

$\begin{gathered} E(Y)=0+9+4.8+1.7 \\ E(Y)=15.5 \end{gathered}$

The expected value is 15.5

Answer: 15.5