GATE Electronics and Communications (EC) 2019 Solved Paper

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Question : 25 of 65

Marks: +1, -0

If

X

and

Y

are random variables such that

E[2 X+Y]=0

and

E[X+2 Y]=33

, then

E[X]+E[Y]=

____________.

Your Answer:

Solution:

We know that

E[A X+B Y]=A E[X]+B E[Y]

∴ {E}[2 {X}+ {Y}]=2 {E}[ {X}]+ {E}[ {Y}]=0

.....(i)

And

E[X+2 Y]=E[X]+2 E[Y]=33

.....(ii)
Adding (i) and (ii)

3 E[X]+3 E[Y]=33

∴ {E}[ {X}]+ {E}[ {Y}]=11

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