Homework SourseX and Y have the following joint probability mass function F
X and Y have the following joint probability mass function
For jointly distributed random variables X and Y E[X|Y=2] =
| Y | ||||
| 1 | 2 | 3 | ||
| 2 | 0.08 | 0.12 | 0.10 | |
| X | 5 | 0.13 | 0.15 | 0.05 |
| 7 | 0.12 | 0.20 | 0.05 |
Solution
We get P(x|y = 2) by dividing the P(x = a, y = 2) value by 0.47 (0.12+0.15+0.20).
Consider:
=E(x|y=2)
Hence,
E(x|y = 2) = 5.085106 [ANSWER]
| x | P(x|y=2) | x P(x|y=2) |
| 2 | 0.255319 | 0.510638 |
| 5 | 0.319149 | 1.595745 |
| 7 | 0.425532 | 2.978723 |
![X and Y have the following joint probability mass function For jointly distributed random variables X and Y E[X|Y=2] = Y 1 2 3 2 0.08 0.12 0.10 X 5 0.13 0.15 0.](/WebImages/35/x-and-y-have-the-following-joint-probability-mass-function-f-1105933-1761585328-0.webp "X and Y have the following joint probability mass function For jointly distributed random variables X and Y E[X|Y=2] = Y 1 2 3 2 0.08 0.12 0.10 X 5 0.13 0.15 0.")
