Nikita has three coins. One coin is fair, one coin is biased so that the probability of obtaining a head is $$\(\frac{1}{3}\)$$ and the third coin is biased so that the probability of obtaining a head is $$\(\frac{1}{5}\)$$. The random variable $$\(X\)$$ is the number of heads that Nikita obtains when he throws all three coins at the same time. Find the probability generating function of $$\(X\)$$. ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . Rajesh has two fair six-sided dice with faces labelled $$\(1,2,3,4,5,6\)$$. The random variable $$\(Y\)$$ is the number of 4s that Rajesh obtains when he throws the two dice. The random variable $$\(Z\)$$ is the sum of the number of heads obtained by Nikita and the number of 4 s obtained by Rajesh.

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