1. Use the built-in keyboard: open the math application or calculator application, and directly enter the math expression of the expected value in the input box. For example, if you want to input the symbol e of the expected value, you can directly find the corresponding letter e on the keyboard to input it.

2. Use third-party mathematical input tools: You can search and download some application programs specially used for mathematical input in the App-Store, such as Mathway, Symbolab, etc. These applications usually provide more input options for mathematical symbols and formulas, which facilitates the input of complex mathematical expressions.

3. Input with a stylus: Use a pen or stylus that supports handwriting function on the iPad, and the built-in handwriting function can be used to input mathematical expectation values. Open any application that supports handwriting input, select handwriting mode, and write down the mathematical expression of expected value in the blank area.