Problem 5.1 Bias and variance of the kernel density estimator

In this problem, we will derive the bias and variance of the kernel density estimator. Let $X = \{x_1, \cdots, x_n\}$ be the r.v. samples, drawn independently according to the true density $p(x)$.

(a) Show that the mean of the estimator is

$$\mathbb{E}_X[\hat{p}(x)] = \int p(\mu)\tilde{k}(x - \mu)d\mu = p(x) * \tilde{k}(x), \quad (5.1)$$

where $*$ is the convolution operator. What does this tell you about how the KDE is biased?