![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-π-and-π-are-random-variables-such-that-πΈ2π-π-0-and-πΈπ-2π-33-then-πΈπ-πΈπ-.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 ‘x’
Application:
E[2x + y] = 0
2E[x] + E[y] = 0Β Β Β —-(1)
E[x + 2y] = 33
E[x] + 2E[y] = 33Β Β Β Β —-(2)
Adding (1) and (2)
3E[x] + 3E[y] = 33
E[X] + E[Y] = 11
![If π and π are random variables such that πΈ[2π + π] = 0 and πΈ[π + 2π] = 33, then πΈ[π] + πΈ[π] =Β](https://www.gkseries.com/blog/wp-content/uploads/thumbs_dir/In-the-circuit-shown-A-and-B-are-the-inputs-and-F-is-the-output.-What-is-the-functionality-of-the-circuit-qaga8560mobi9u32yhw68dy0u5w4lnv80iqjt0tav0.jpg)
![If π and π are random variables such that πΈ[2π + π] = 0 and πΈ[π + 2π] = 33, then πΈ[π] + πΈ[π] =Β](https://www.gkseries.com/blog/wp-content/uploads/thumbs_dir/Durand-Cup-2023-Schedule-qagbhgxu72da4w8ua38igy6832hbs7t8wv9gxdlut8.jpg)
![Determine the correctness (or otherwise) of the following Assertion [A] and the Reason [R]](https://www.gkseries.com/blog/wp-content/uploads/2023/10/Determine-the-correctness-or-otherwise-of-the-following-Assertion-A-and-the-Reason-R.jpg)
