2. a. Suppose that \( X \) has a binomial distribution with probabillity distribution given as follows. Prove that \( E(X)=n \theta \). \[ f(x)=\binom{n}{x} \theta^{x}(1-\theta)^{n-x} \quad x=0,1,2 \ldots n \] [5 marks]
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Step 1: Recall the definition of the expected value for a discrete random variable \( X \) with probability mass function \( f(x) \): \[ E(X) = \sum_{x=0}^{n} x \cdot f(x) \] Show more…
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