True or False: Interaction variables violate the Gauss Markov assumption that our model should be linear in parameters

(6) Population Modeling with Discrete Dynamical Linear Systems. We now discuss populations with discrete breeding seasons, where reproduc- tion is limited to a particluar season of the year. For example, let's consider the number of female ruby-throated hummingbirds in a population with an annual breeding season of March to July. A female usually lays one clutch of two eggs; sometimes two clutches are laid. We will assume that the average life span of a female hummingbird is four years. We define the age of a bird at the END of a breeding season as follows: age zero (0) : any bird that is born during the current breeding season age one (1): any zero-year old bird which survives to the end of the next breeding season age two (2): any one-year old bird which survives to the end of the next breeding season age three (3): any two-year old bird which survives to the end of the next breeding season We make the following assumptions about the reproductive viability of female birds: age zero…

if matrix A= [[a,1-b],[1-a,b]] Assume A does not equal the idenituty . what is the steady state vector for matrix A

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Question 4(a) Assume that the probability of rain tomorrow is 0.5 if it is raining today, and assume that the probability of its being clear (no rain) tomorrow is 0.9 if it is clear today. Also assume that these probabilities do not change if information is also provided about the weather before today.(i) Explain why the stated assumptions imply that the Markovian property holds for the evolution of the weather. (ii) Formulate the evolution of the weather as a Markov chain by defining its states and giving its (one-step) transition matrixb) i. consider the M/M/1 queue with arrival rate λ and service rate µ and explain how it can be modelled as a birth death model. ii. For the M/M/1 queue derive the form of , the equilibrium distribution of the number of customers present, and give any conditions needed to ensure the existence of the equilibrium distribution. Derive the mean value of the equilibrium distribution d) If an M/D/1 queue has utilization of 80% do you expect its mean queue…