Please solve the following quesiton with steps. Copying answers from others will receive a negative feedback, thank you!

BB-standard Brownian bridge,BM-standard Brownian motion, GP-Gaussian process H1 Let B = (B.) be BM. Determine the following quantities: (a) E[2B2 - Bil; (b) E[(2B1 - B2)']; (c) a Lebesgue density of (B2 - Bi)?; (d) E[B3|B2]; (e) the distribution of 2-B2-Ba by computing Elexp(10(2-B2 - B3))], 0 ER; (f) P(limn +oo BI = 1) (here n E N)