Let Z(t),t 0, be the standard Brownian process. Show that has zero mean and variance
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Let Z(t),t ≥ 0, be the standard Brownian process. Show that
![T [" t [Z(u) - Z(t)] du](https://dsd5zvtm8ll6.cloudfront.net/images/question_images/1700/4/6/5/330655b0ab2dabe41700465330095.jpg)
has zero mean and variance σ2(T − t)3/3.
![Consider T var ar [Z(u) Z(1)] du - T T = E[[" [Z(u) Z(1)][Z(v) Z(1)]dudv] E[{Z(u) Z(t)}{Z(v) Z(t)}] dudv](https://dsd5zvtm8ll6.cloudfront.net/images/question_images/1700/4/6/5/383655b0ae797c4a1700465381656.jpg)
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