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The video writes both $E(x)$ and $\mu$ because they represent the same quantity: the expected value of the random variable, which is also called the population mean. The speaker uses these notations interchangeably to emphasize that the sample mean converges to this fixed theoretical value.

Conditions: The random variable has an expected value.; $E(x)$ and $\mu$ are used as alternative notations for the population mean.

The video writes both $E(x)$ and $\mu$ because they represent the same quantity: the expected value of the random variable, which is also called the population mean. The speaker uses these notations interchangeably to emphasize that the sample mean converges to this fixed theoretical value.

Conditions: The random variable has an expected value.; $E(x)$ and $\mu$ are used as alternative notations for the population mean.