Let the joint probability density function of two discrete random X and Y be given as:
| X | |||||
|---|---|---|---|---|---|
| 2 | 3 | 4 | 5 | ||
| Y | 0 | 0 | 0.03 | 0 | 0 |
| 1 | 0.34 | 0.30 | 0.16 | 0 | |
| 2 | 0 | 0 | 0.03 | 0.14 | |
ii) Find the marginal distribution of X and Y.
iii) Find the conditional distribution of X given .
iv) Test the independence of variable s X and Y.
Let , where
and
Find the distribution of:
v) Find .
Marginal distribution of X: [ P_X(2) = 0 + 0.34 + 0 = 0.34 ] [ P_X(3) = 0.03 + 0.30 + 0 = 0.33 ] [ P_X(4) = 0 + 0.16 + 0.03 = 0.19 ] [ P_X(5) = 0 + 0 + 0.14 = 0.14 ] So, (P_X = {2:0.34, 3:0.33, 4:0.19, 5:0.14}). Marginal distribution of Y: [ P_Y(0) = 0 + 0.03 + 0 + 0 = 0.03 ] [ P_Y(1) = 0.34 + 0.30 + 0.16 + 0 = 0.80 ] [ P_Y(2) = 0 + 0 + 0.03 + 0.14 = 0.17 ] So, (P_Y = {0:0.03, 1:0.80, 2:0.17}). Conditional distribution of X given (Y=1): ___ ____ ____ ________ ______.
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.
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Let the joint probability density function of two discrete random X and Y be given as:
| X | |||||
|---|---|---|---|---|---|
| 2 | 3 | 4 | 5 | ||
| Y | 0 | 0 | 0.03 | 0 | 0 |
| 1 | 0.34 | 0.30 | 0.16 | 0 | |
| 2 | 0 | 0 | 0.03 | 0.14 | |
iii) Find the conditional distribution of X given .
v) Find .