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A basketball player has a theoretical free-throw success rate of \(p = 0.8\). We define a random variable \(X_i=1\) if the shot is made and \(X_i=0\) if it is missed.
If the player takes \(n=1000\) shots, what does the sample mean \(\overline{X}_{1000}\) represent in this context?
Using the Law of Large Numbers, predict the value of \(\overline{X}_n\) if the player takes an infinite number of shots.
Explain why the player might make 5 shots in a row (100\(\pourcent\) success rate for that short sequence) despite the long-term average being 80\(\pourcent\).
Capture an image of your work. AI teacher feedback takes approximately 10 seconds.
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