If now we have a nonlinear dynamical system dx/dt=f(x) and we use MC to evolve an ensemble of realizations x1,x2,...,xm in time, but we want to apply the filtering step of the Kalman filter (just KF, no EnKF) anyway when data y|x~N(Hx, R) is collected, what extra step(s) do we need compared to the standard KF for a linear system?

You are constructing a histogram for scores that range from 70 to 100 in whole points. frequencies range from 3 to 10; that is, every whole-point score between 60 and 100 occurs at least 3 times, and at least one score occurs 10 times. which of these would probably be the best range and size for the score intervals along the x-axis?

Monthly water bills for a city have a mean of $108.43 and a standard deviation of $32.09. find the probability that a randomly selected bill will have an amount greater than $155, which the city believes might indicate that someone is wasting water. would a bill that size be considered unusual?

3women sell hats at a craft fair weekly. the money they make at the fair is split into categories. 9% goes to pay taxes. $55 goes to pay rent for the space they sell in. the rest is split between the women. if the group make $706 at the fair, how much does each women get paid once the money is divided