For a standard one-dimensional Brownian motion $W(t)$, calculate:
$$E\bigg[\Big(\frac{1}{T}\int\limits_0^TW_t\, dt\Big)^2\bigg]$$
Note: I am not able to figure out how to approach this problem. All i can think of is that the term $\frac{1}{T}\int\limits_0^TW_t\,dt$ is like 'average'. But not sure how to proceed ahead. I'm relatively new to Brownian motion. I tried searching the forum for some hints..but could not find one. I will really appreciate if you could please guide me in the right direction. Thanks!