3. A certain basketball player is excellent at free-throw shooting and makes p = 0.9 of her free throws. Assume that we can treat these as Bernoulli trials and let X equal the number of attempts needed to make r = 8 free throws. What is the probability that the sequence ends exactly at 12th trial?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
probability that the player makes a free throws successfully = 0.9
Define the Random Variable,
X : Number of attempts needed to make 8 successful free throws.
So, X ~ Negative Binomial(r=8,p=0.9)
So, PMF of X
P(X=x) =
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