The following is an interview question taken from Mark Joshi et al. Quant job interview book.
Question: What is the correlation between $2$ Brownian motions at time $t_1$ and $t_2?$ Assume that they are jointly normal with correlation $\rho.$
Initially I thought that we are asked to find correlation between $B_{t_1}$ and $B_{t_2}$ where $(B_t)_t$ is a Brownian motion. By using correlation formula, we have the correlation is $$\frac{Cov(B_{t_1},B_{t_2})}{\sigma_{B_{t_1}}\sigma_{B_{t_2}}} = \frac{\min(t_1,t_2)}{\sqrt{t_1}\sqrt{t_2}}.$$
However, the answer given is $$\rho \sqrt{\frac{\min(t_1,t_2)}{\max(t_1,t_2)}}.$$
I think I do not understand the question.
It would be good if someone can clarify the question for me.