Hello. Please solve question nr.1

The state evolution model allows us to model the relationship between the object state at the tth measurement and its state at the (t+1)th measurement. In particular, if the time difference At between t and t +1 is small enough and that the velocity is almost constant, we have 2(t+1) = x(t) +v(t) At + n(4+1), (1) (t+1) where v(t+1) is the velocity of the object at time (t + 1) and not is a modeling error term, assumed to be zero-mean Gaussian with variance oz. Note that here we assume At = .01 (we (t+1) receive a measurement every 10ms) and that na is assumed to be independent of the other terms in Eq. (1). Question 1: Under these hypotheses, write the expression of the probability density function f(x:(t+1)]z (6), vlt), o?). What are its mean and its variance? (4 Marks) The state evolution model allows us to model the relationship between the object state at the tth measurement and its state at the (t+1)th measurement. In particular, if the time difference At between t and t +1 is small enough and that the velocity is almost constant, we have 2(t+1) = x(t) +v(t) At + n(4+1), (1) (t+1) where v(t+1) is the velocity of the object at time (t + 1) and not is a modeling error term, assumed to be zero-mean Gaussian with variance oz. Note that here we assume At = .01 (we (t+1) receive a measurement every 10ms) and that na is assumed to be independent of the other terms in Eq. (1). Question 1: Under these hypotheses, write the expression of the probability density function f(x:(t+1)]z (6), vlt), o?). What are its mean and its variance? (4 Marks)