X and Y are random variables with E [X]=E[Y]=0 and Var[X]=1, Var[Y]=4 and correlation coefficient p=1/2. Find Var[X+Y].

Daniella Reyes

Daniella Reyes

Answered question

2022-09-21

X and Y are random variables with E [X]=E[Y]=0 and Var[X]=1, Var[Y]=4 and correlation coefficient p=1/2. Find Var[X+Y].

Answer & Explanation

Abagail Stephenson

Abagail Stephenson

Beginner2022-09-22Added 9 answers

C o v [ X , Y ] = ρ V a r [ X ] V a r [ Y ] = 1
V a r [ X + Y ] = V a r [ X ] + V a r [ Y ] + 2 C o v [ X , Y ] = 1 + 4 + 2 ( 1 ) = 7
Result:
V a r [ X + Y ] = 7

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