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10 cards from this deck
Number of failures before achieving rrr successes in Bernoulli trials
P(Y=x)=(x+r−1r−1)pr(1−p)xP(Y=x)=\binom{x+r-1}{r-1}p^r(1-p)^xP(Y=x)=(r−1x+r−1)pr(1−p)x
Fixed number of successes
Probability of success in a single trial
Number of failures before achieving rrr successes
μ=r(1−p)p\mu = \frac{r(1-p)}{p}μ=pr(1−p)
σ2=r(1−p)p2\sigma^2 = \frac{r(1-p)}{p^2}σ2=p2r(1−p)
P(X≥r)P(X \geq r)P(X≥r) where X∼Bin(n,p)X \sim \text{Bin}(n, p)X∼Bin(n,p)
NegBin: failures before rrr successes; Bin: successes in nnn trials
Y∼NegBin(r,p)Y \sim \text{NegBin}(r, p)Y∼NegBin(r,p)
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