Calculating the Expected Value for a Continuous Uniform Distribution: Formula and Example

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

The expected value (also known as the mean or the average) for a continuous uniform distribution can be calculated using the following formula:

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

Where:
– E(X) is the expected value
– a is the lower limit of the distribution
– b is the upper limit of the distribution

To calculate the expected value, simply substitute the values of a and b into the formula

The expected value (also known as the mean or the average) for a continuous uniform distribution can be calculated using the following formula:

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

Where:
– E(X) is the expected value
– a is the lower limit of the distribution
– b is the upper limit of the distribution

To calculate the expected value, simply substitute the values of a and b into the formula.

Let’s look at an example:
Suppose we have a continuous uniform distribution with a lower limit (a) of 3 and an upper limit (b) of 9. We want to calculate the expected value.

E(X) = (a + b) / 2
E(X) = (3 + 9) / 2
E(X) = 12 / 2
E(X) = 6

So, the expected value for this continuous uniform distribution is 6.

In general, for any continuous uniform distribution, regardless of the specific values of a and b, the expected value will always be the average of the lower and upper limits.

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