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\textbf{Aufgabe 1}\\  $\mathbb{E}_\theta[\sum_{i=1}^{n}a_ix_i]=\sum_{i=1}^na_i\mathbb{E}_{\theta}[X_i]=\mathbb{E}_\theta[X_1]*\sum_{i=1}^na_i\\  \\  => \mathbb{E}_\theta[\sum_{i=1}^{n}a_ix_i]=\mathbb{E}_\theta[X_1] <=> \mathbb{E}_\theta[\sum_{i=1}^{n}a_ix_i]=\mathbb{E}_\theta[X_1]\ <=>\  \sum_{i=1}^na_i=1$