Question: Make up a Binomial (Bernoulli) Experiment so that the probability of getting 7 successes is \(\left( \begin{matrix} 12 \\ 7 \\ \end{matrix} \right){{\left( \frac{1}{4} \right)}^{4}}\times {{\left( \frac{3}{4} \right)}^{5}}\). Write it up as if you were the professor writing an exam question (a word problem). the answer to which is that probability. Let X be the random variable associated with this experiment, find the expected value of X and explain what that means in the context of your experiment.

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