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X and Y are two random variables for which joint pdf is given by P(x=i, y=j) = c (i+j) i=1, 2, 3, 4; j=1, 2, 3 find c and conditional mean and variance of X given Y=1.

Mumbai University > Electronics and Telecommunication > Sem5 > Random Signal Analysis

Marks: 10M

Year: Dec 2014

1 Answer
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X and Y are discrete RVs

To find c:

We can tabulate the probabilities as follows:

P( x=i,y=j ) = c( i + j)       1≤x≤4,1≤y≤3

X╲Y 1 2 3 Total
1 2c 3c 4c 9c
2 3c 4c 5c 12c
3 4c 5c 6c 15c
4 5c 6c 7c 18c …

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