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question 2.3 of assignment x2

Which bit of the solution do you not get? Try and explain what you're thinking.
 
Here the question takes wts of individual compound distribution S and T to derive distribution of U.But in getting distribution of u taking u=1,2 solution is not clear. Kindly clarify that segment.
 
The answer just applies the formula 3/5*P(S=x)+2/5*P(T=x).

So for u=1 we have 3/5*P(S=1)+3/5*P(T=1), which gives 3/5*1/3 + 2/5*1/2.

Similarly for u=2 we have 3/5*P(S=2)+3/5*P(T=2), which gives 3/5*1/3 + 2/5*1/2.
 
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