Let X(t) be a Poisson process of rate 3. Find the following, giving your answer to 2 decimal places: P(X(1) = 0) = P(X(0.5) = 2) = P(X(9) - X(8) = 0) = P(X(1) = 11 | X(0.5) = 9) = E(X(3)) = E(X(11)X(9)) =

bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.

Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?

The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is given by A(t)=a(e)rt, where a is the amount ofprincipal initially deposited into an account thatcompounds continuously. Prove that the percentageof interest earned to principal at any time t can becalculated with the formula I(t)=ert1.