7. Let Wt be a standard Brownian Motion. Define X, is by X₁ =W², t≥ 0. a) Is Xt a Brownian Motion? b) Compute the probability density function fx(x) of X₁. c) Compute E[(X₁), E (Xt+s – Xt), and E[(Xt+s – Xt)²] (here t≥ 0, s ≥ - 0). d) Compute E [X₁ (Xt+s – Xt)²]. Does the process X₂ have independent increments?

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