I need to show that (W(adsbygoogle = window.adsbygoogle || []).push({}); _{t})^{2}is a brownian motion

So let V_{t}= (W_{t})^{2}

I need to first show that V_{t+s}- V_{s}~ N(0,t)

V_{t+s}- V_{s}= (W_{t+s})^{2}- (W_{s})^{2}= (W_{t+s}+ W_{s})(W_{t+s}- W_{s})

(W_{t+s}- W_{s}) ~ N(0,t)

But is (W_{t+s}+ W_{s}) ~ N(0,t)?

If it is what happens when I multiply two RV's that are normally distributed together? What can I say about the variance of the new distribution?

Thanks

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# Brownian Motion question

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