Write the formula for E(X) and Var(X)

To solve this question, let’s define what \(E(X)\) and \(Var(X)\) represent and write their formulas in detail.

### Expectation (\(E(X)\)):
\(E(X)\), or the expected value of a random variable \(X\), represents the mean or average value of \(X\). It is calculated as follows:

1. **For a discrete random variable:**
\(E(X) = \sum_{x} x \cdot P(X = x)\)
Here:
- \(x\) are the possible values of the random variable.
- \(P(X = x)\) is the probability of each value.

2. **For a continuous random variable:**
\(E(X) = \int_{-\infty}^{\infty} x \cdot f(x) dx\)
Here:
- \(f(x)\) is the probability density function of the random variable \(X\).

### Variance (\(Var(X)\)):
The variance measures the spread or variability of the random variable \(X\) around its mean. The formula is:

1. **General formula:**
\(Var(X) = E[(X - \mu)^2]\), where \(\mu = E(X)\).

2. **Simplified form:**
\(Var(X) = E(X^2) - [E(X)]^2\)
Here:
- \(E(X^2)\) is the expected value of \(X^2\).
- \([E(X)]^2\) is the square of the mean.

By calculating \(E(X)\) and \(E(X^2)\), you can compute \(Var(X)\). Let me know if you need further clarification or an example.