Let $X_1, X_2, X_3, Y_1, Y_2, Y_3, Z_1, Z_2, Z_3$ be random variables which have uniform distribution between 0 and 1. It means, the average of $X_1 = 0.5$
Let: $X=X_1 + X_2 + X_3,$
$Y=Y_1 + Y_2 + Y_3$, $Z=Z_1 + Z_2 + Z_3$
In this case, the probability of $\{X$ is bigger than $Y$ and $Z$ both$\}$ would be $\dfrac{1}{3}$.
My question is:
What is the probability of "$c+X$ is bigger than $Y$ and $Z$" when $c$ is a constant"?
For example: what is $\mathbb{P}\left[0.2+X >\max\{Y,Z\}\right]$?
Best Answer
HINT