The table below shows a joint probability distribution of two discrete random variables X and Y....

 

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The table below shows a joint probability distribution of two discrete random variables X and Y. X 0 1 Y -1 0.3 0.1 0 0.1 b 1 0.2 0.2 (i) Find b that gives a valid the joint probability distribution. (ii) Using the value of b from (i), determine whether these two random variables are indepen- dent. (iii) Find a such that Ja(3-2), 0 2 f(z) = 0, otherwise represents a probability density function of random variable Z, and compute P(1 Z 3). The table below shows a joint probability distribution of two discrete random variables X and Y. X 0 1 Y -1 0.3 0.1 0 0.1 b 1 0.2 0.2 (i) Find b that gives a valid the joint probability distribution. (ii) Using the value of b from (i), determine whether these two random variables are indepen- dent. (iii) Find a such that Ja(3-2), 0 2 f(z) = 0, otherwise represents a probability density function of random variable Z, and compute P(1 Z 3).