Question

Find the expected value E(x) of the following data. Round your answer to one decimal place.

x 4 5 6 7 8
p(x=x) 0.3 0.2 0.1 0.2 0.2

Answer 1

The expected value E(x) for the provided data is 5.8 when rounded to one decimal place. It is calculated by multiplying each value of x by its probability and summing all the products.

Step-by-step explanation:

To find the expected value E(x) of the given data, we multiply each value of the random variable by its respective probability and then sum up all the products. This is represented by the formula E(X) = μ = Σ xP(x).

We have the following data:

• x = 4, P(x=4) = 0.3
• x = 5, P(x=5) = 0.2
• x = 6, P(x=6) = 0.1
• x = 7, P(x=7) = 0.2
• x = 8, P(x=8) = 0.2

Now we calculate x*P(x) for each value of x:

• 4 * 0.3 = 1.2
• 5 * 0.2 = 1.0
• 6 * 0.1 = 0.6
• 7 * 0.2 = 1.4
• 8 * 0.2 = 1.6

Finally, we sum these products to get the expected value:

E(X) = 1.2 + 1.0 + 0.6 + 1.4 + 1.6 = 5.8

The expected value or mean of the random variable X, to one decimal place, is 5.8.