What are the assumptions of the geometric growth model? Select all correct answers. Birth and death rates are constant Birth and death rates are density-dependent Different individuals have different ) values ) depends on variable birth and death rates Individuals are identical4. Vehicles arrive at a car wash station according to the Poisson process An average of 2,5 vehicles per hour arrive at this car wash station If the washing in the parking orea washing a vehicle takes an average of 12.5 minutes, and the washing Times of the vehicles correspond to the exponential distribution? a-) Express the process as a birth-death process, draw a transition rate diagram. Determine the rode of "birth" and the rate of "death" b) what are the chances that the system is empty? (-) what are the chances of up to 2 cars at the car wash station? 1-) what are the chances of an incoming vehicle waiting?4. Which is true of the Gaussian function? a. One way of computing the derivative of noisy signal is to smooth with a Gaussian before taking the derivative. Now, because differentiation and convolution are both linear operators we can invert their order and thereby compute the derivative of the smoothed signal by simply convolving the raw signal with the derivative of a Gaussian. b. Gaussian filtering in 2D can be decomposed into two 10 Gaussian filtering operations. c. Convolution of a signal with a Gaussian filter in the spatial domain equates with multiplication of the Fourier transform of the signal with the Fourier transform of the Gaussian (which is a Gaussian also) in k-space. d. A Gaussian filter acts as a low-pass filter. e. All of the above are true