If π and π are random variables such that πΈ[2π + π] = 0 and πΈ[π + 2π] = 33, then πΈ[π] + πΈ[π] =Β
![If π and π are random variables such that πΈ[2π + π] = 0 and πΈ[π + 2π] = 33, then πΈ[π] + πΈ[π]](https://www.gkseries.com/blog/wp-content/uploads/2023/08/If-%F0%9D%91%8B-and-%F0%9D%91%8C-are-random-variables-such-that-%F0%9D%90%B82%F0%9D%91%8B-%F0%9D%91%8C-0-and-%F0%9D%90%B8%F0%9D%91%8B-2%F0%9D%91%8C-33-then-%F0%9D%90%B8%F0%9D%91%8B-%F0%9D%90%B8%F0%9D%91%8C--1024x536.jpg)
Q. If π and π are random variables such that πΈ[2π + π] = 0 and πΈ[π + 2π] = 33, then πΈ[π] + πΈ[π] =Β Β Β Β Β Β Β Β Β Β .
Ans:11
Solution:
E[x + y] = E[x] + E[y]
E [Ax] = A E[x]
Where E [x] represents the expected or mean value of the random variable βxβ
Application:
E[2x + y] = 0
2E[x] + E[y] = 0Β Β Β β-(1)
E[x + 2y] = 33
E[x] + 2E[y] = 33Β Β Β Β β-(2)
Adding (1) and (2)
3E[x] + 3E[y] = 33
E[X] + E[Y] = 11