I give you a function rand that returns a number chosen uniformly at random from [0, T] for some number T that you don’t know. Your task is to approximate T. You do this by calling rand 100 times, recording the results as X_{1}, X_{2}, \ldots, X_{100}, and guessing
\hat{T}=\alpha \cdot \max \left\{X_{1}, X_{2}, \ldots, X_{100}\right\}
for some \alpha. Which value of \alpha ensures that \mathbb{E}[\hat{T}]=T?