Representing the Probability Distribution of XY in a Graph

[Alexsandro]

Could someone help me to find the probability distribution de XY below ?
Take $$\Omega$$ to be a set of 5 real numbers. Define a probability measure and a random variable X on it which takes the values 1, 2, 3, 4, 5 with probability $\frac{1}{10}, \frac{1}{10}, \frac{1}{5}, \frac{1}{5}, \frac{2}{5},$ respectively; another random variable Y which takes the values $\sqrt{2}, \sqrt{3}, \pi$ with probabilities $\frac{1}{5}, \frac{3}{10}, \frac{1}{2}$. Find the probability distribution of XY.

 

[Hurkyl]

Well, where are you stuck? What have you done, and what do you think you need to do?

 

[HallsofIvy]

Just go ahead and do it! Since one possible value for x is 1 (with probability 1/10) and one possible value for y is $\sqrt{2}$ (with probability 1/5, one possible value for xy is $1*\sqrt{2}= \sqrt{2}$ with probability (1/10)(1/5)= 1/50. There are 15 possible values for xy. Calculate each of them.

 

[Alexsandro]

thanks

Just go ahead and do it! Since one possible value for x is 1 (with probability 1/10) and one possible value for y is $\sqrt{2}$ (with probability 1/5, one possible value for xy is $1*\sqrt{2}= \sqrt{2}$ with probability (1/10)(1/5)= 1/50. There are 15 possible values for xy. Calculate each of them.

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Thank you, for help. One doubt, that I have, consists of knowing the best way to represent the probability distribution on this situation: for a graph or correspondence between points ?