9.7 Let Xi be distributed as a normal with mean i and variance 2, where 1 <

9.7 Let Xi be distributed as a normal with mean μi and variance σ2, where μ1 <

μ2 < ··· < μn <... . Let ℱi = σ(Xi) the sigma algebra generated by the random variable Xi.

a) Is ℱ = {ℱi}i a filtration?

b) If it is not, how can we modify it so that it becomes a filtration for the stochastic process X = {Xi}?

c) Is X = {Xi} stationary? Does it have independent components?

d) Does X = {Xi} have stationary increments? Does it have independent increments?