What's the covariance of $B_t$ and $B_{t^2}$, where $B_t$ is the standard Brownian Motion?

Question

What's the covariance of $B_t$ and $B_{t^2}$, where $B_t$ is the standard Brownian Motion?

$B_t$ is the standard Brownian Motion, what's $\operatorname{Cov}(B_t,B_{t^2})$?

Answer 1

Hint: $B_t$ is a normal random variable. Express the covariance in terms of the moments of a standard normal random variable, and then look those up.