Solve the probability distribution and expectation problem

chwala
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Homework Statement
See attached
Relevant Equations
understanding of probability distribution concept...
This is the problem;

1635598062807.png


Find my working to solution below;
1635598109409.png

1635598140494.png
find mark scheme solution below;

1635598182806.png


I seek any other approach ( shorter way of doing it) will be appreciated...
 
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chwala said:
Homework Statement:: See attached
Relevant Equations:: understanding of probability distribution concept...

shorter way of doing it
It would have been quicker to have found the probability of Y=2 by subtracting the other two probabilities from 1. I don't see any other shortcuts.
 
haruspex said:
It would have been quicker to have found the probability of Y=2 by subtracting the other two probabilities from 1. I don't see any other shortcuts.
That's true, but it could pose problem to a student who may have made a mistake on say finding wrong values of ##Y=0 ##& ##Y=4##, ...if you get what I mean... this error would consequently affect the value of ##Y=2##.
Finding the values of ##Y## indepedently and then checking whether their total sum is ##1## is more concrete...
 
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