4.2 Mean Or Expected Value And Standard Deviation - Statistics

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A men's soccer team plays soccer zero, one, or two days a week. The probability that they play zero days is .2, the probability that they play one day is .5, and the probability that they play two days is .3. Find the long-term average or expected value, μ, of the number of days per week the men's soccer team plays soccer.

To do the problem, first let the random variable X = the number of days the men's soccer team plays soccer per week. X takes on the values 0, 1, 2. Construct a PDF table adding a column x*P(x), the product of the value x with the corresponding probability P(x). In this column, you will multiply each x value by its probability.

x P(x) x*P(x)
0 .2 (0)(.2) = 0
1 .5 (1)(.5) = .5
2 .3 (2)(.3) = .6
Table 4.5 Expected Value Table This table is called an expected value table. The table helps you calculate the expected value or long-term average.

Add the last column x*P(x) x*P(x) to get the expected value/mean of the random variable X.

E(X)=μ=∑xP(x)=0+.5+.6=1.1 E(X)=μ=∑xP(x)=0+.5+.6=1.1

The expected value/mean is 1.1. The men's soccer team would, on the average, expect to play soccer 1.1 days per week. The number 1.1 is the long-term average or expected value if the men's soccer team plays soccer week after week after week.

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