1. The problem is to write the formula for the expected value $E(X)$ of a continuous random variable $X$. 2. The expected value is defined as the integral of $x$ times its probability density function $f(x)$ over the entire real line. 3. The formula is: $$E(X) = \int_{-\infty}^{\infty} x f(x) \, dx$$ 4. Here, $f(x)$ is the probability density function of $X$, and the integral sums over all possible values of $x$ weighted by their probabilities. 5. This formula is fundamental in probability theory and statistics for finding the mean or average value of a continuous random variable.