Questions: Consider the following data: x 4 5 6 7 8 P(X=x) 0.1 0.1 0.2 0.2 0.4 Step 1 of 5: Find the expected value E(X). Round your answer to one decimal place.

Consider the following data:
x 4 5 6 7 8
P(X=x) 0.1 0.1 0.2 0.2 0.4

Step 1 of 5: Find the expected value E(X). Round your answer to one decimal place.

Transcript text: Consider the following data: \begin{tabular}{|c|c|c|c|c|c|} \hline $\boldsymbol{x}$ & 4 & 5 & 6 & 7 & 8 \\ \hline $\boldsymbol{P}(\boldsymbol{X}=\boldsymbol{x})$ & 0.1 & 0.1 & 0.2 & 0.2 & 0.4 \\ \hline \end{tabular} Copy Data Step 1 of 5: Find the expected value $E(X)$. Round your answer to one decimal place. AnswerHow to enter your answer (opens in new Keypad window) Keyboard Shortcuts 2 Points

Solution

Solution Steps

Step 1: Multiply each outcome by its corresponding probability

For outcome 4 with probability 0.1, the product is 0.4.
For outcome 5 with probability 0.1, the product is 0.5.
For outcome 6 with probability 0.2, the product is 1.200.
For outcome 7 with probability 0.2, the product is 1.400.
For outcome 8 with probability 0.4, the product is 3.2.

Step 2: Sum all the products to find the expected value

The sum of all products is 6.7.

Step 3: Round the expected value to the specified number of decimal places

The expected value rounded to 1 decimal places is 6.7.

Final Answer:

The expected value \(E(X)\) of the discrete random variable \(X\) is approximately 6.7.

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