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Question of interest: P[X1 = 0.1, X2 = 0.2] = ? P[0.3 <= X1 <= 0.6, 0.4 <= X2 <= 0.7] = ?

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Question of interest: P[X1 = 0.1, X2 = 0.2] = ? P[0.3 <= X1 <= 0.6, 0.4 <= X2 <= 0.7] = ?

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  1. Example: You were approached by some microbial ecologists to study the dynamics of microbes in the human body. They chose the mouth and they are pretty sure that there are two species living there (more like 200 I believe). The goal is to study the composition of a bacterial population at a point in time. Those ecologists can observe the proportions of the different species. You want to help them construct a model that will allow them to evaluate the probability of different scenarios of species compositions in samples that they will observe in the future. These researchers believe that the chance of observing these species in the total population is proportional to the product of their concentration. Question of interest: P[X1 = 0.1, X2 = 0.2] = ? P[0.3 <= X1 <= 0.6, 0.4 <= X2 <= 0.7] = ? P[0.1 <= X1 <= 0.2, X2 <= 0.3] = ? P[0.1 <= X1 <= 0.2] = ? P[X2 <= 0.3] = ? P[X1 >= X2] = ? P[0.1 <= X1 <= 0.2 | X1 = 0.3] = ?

  2. x2 (0,1) (1,1) (0,0) x1 (1,0)

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