A company manufactured six television sets on a given day, and these TV sets were inspected for being good or defective.

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A company manufactured six television sets on a given day, and
these TV sets were inspected for being good or defective. The
results of the inspection follow. Defective, Good, Defective,
Defective, Good, Good. Show all possible samples of size four. Let
𝑝𝑝̂ be the sample proportion of good television sets. a. Find the
sampling distribution of 𝑝𝑝̂. b. Based on the sampling distribution
in part a, find the mean of 𝑝𝑝̂ (i.e., 𝜇𝜇𝑝𝑝�) using the formula
𝜇𝜇𝑝𝑝� =𝐸𝐸(𝑝𝑝̂)=∑𝑝𝑝̂𝑃𝑃(𝑝𝑝̂).