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Let H denote the dummy variable for hospitalisation due to COVID-19. Let V denote the number of vaccinations an individual received. H =0 H =1 V=0 X 0.1 V =1 0.15 0.03 V = 2 0.25 0.02 V =3 0.34 0.01 (a) [2 marks] Find x (b) [2 marks] Find the marginal distribution of Vby specifying its probability mass function. (c) [2 marks] What is the probability that an individual is hospitalised due to COVID-19? (d) [3 marks] Given that John is hospitalised due to COVID-19, what is the probability that he had three vaccinations? (e) [4 marks] Compute E(V| H = 1) and E(V|H = 0) (f) [3 marks] Using part (c) and the law of iterated expectations, compute E(V) (g) [4 marks] Compute Var(V|H = 1) and Var(V|H = 0)