My Math Forum help with RV task

October 8th, 2012, 12:50 PM   #1
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Hi!
Please can u help me a bit with this.

[attachment=0:2mr1ynd7]4 copy.jpg[/attachment:2mr1ynd7]

Thanks
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 October 8th, 2012, 10:50 PM #2 Senior Member   Joined: Aug 2012 Posts: 229 Thanks: 3 Re: help with RV task Hey mysteryplanet. For the first one, you should consider that you want to find the probability of all events where you take an x from X, a y from Y and then you find all the events for some z where x + y = z for a fixed z corresponding to Z = z. Now if all your events are disjoint (i.e. nothing is common with them) then the probability of the union of these events is the sum of these events. So since you are trying to find all the times when x + y = z for all possible combinations of x being in X and y being in Y and since they are all disjoint, then the probability of getting this is adding up all of the individual probabilities to get the final probability. Remember that P(b U c) = P(b) + P(c) if b and c are disjoint and every combination of (x,y) pairs will be disjoint so when you are finding the P(a U b U c ... ) you are adding up the individual probabilities and all of these individual events correspond to getting that z for a given (x,y) pair. For the second one, you should think about the definition of expectation of a discrete random variable.

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