Suppose we have a number of independent random variables of the form $X_1 \sim U[a_1,b_1], X_2 \sim U[a_2,b_2], X_3 \sim U[a_3,b_3]$. Now, suppose we generate a random variable $Y$ as follows:
$$Y = \max_{1 \leq l \leq n} \left(1 - \left(\sum_{i=0}^{l-1} \binom{n}{i} X_1^i \cdot (1-X_1)^{n-i} \right) \cdot (1-X_2^3 \cdot X_3)\right) \cdot \frac{l}{n}$$
I want to find $\mathbb{E}[Y]$. Does it make sense to approach this approach with Monte-Carlo simulation?
Thanks in advance.
Regards.