Calculating the Expected Value for a Continuous Uniform Distribution

Expected value for continuous uniform distribution formula (be able to calculate given values)

The expected value, or mean, of a continuous uniform distribution is given by the formula:

E(X) = (a + b) / 2

where “a” represents the lower bound of the distribution and “b” represents the upper bound of the distribution

The expected value, or mean, of a continuous uniform distribution is given by the formula:

E(X) = (a + b) / 2

where “a” represents the lower bound of the distribution and “b” represents the upper bound of the distribution.

To calculate the expected value, simply substitute the appropriate values of “a” and “b” into the formula. Let’s consider an example:

Suppose we have a continuous uniform distribution with a lower bound (a) of 2 and an upper bound (b) of 7. We can calculate the expected value as follows:

E(X) = (a + b) / 2
E(X) = (2 + 7) / 2
E(X) = 9 / 2
E(X) = 4.5

Therefore, the expected value for this continuous uniform distribution is 4.5.

It’s important to note that the expected value represents the center or average of the distribution. It is not necessarily guaranteed that the actual observed values will be close to the expected value, as the uniform distribution allows for equal likelihood of any value within the specified range.

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