eQuate It CAS UDFs — Discrete Probability (TI-Nspire CAS)
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1. binomsolve(k, p, threshold) — Trials for target probability
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Define binomsolve(k, p, threshold) = Prgm
  Local n, prob
  n := k
  While true
    prob := binomCdf(n, p, k, n)
    If prob >= threshold Then
      Disp "n = ", n
      Disp "P(X >= ", k, ") = ", approx(prob)
      Return n
    EndIf
    n := n + 1
    If n > 10000 Then
      Disp "No solution found within 10000 trials"
      Return -1
    EndIf
  EndWhile
EndPrgm


2. dcondpr — Discrete conditional probability
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(Binomial version)
Define dcondpr(n, p, c1, c2) = Prgm
  Local pC1, pC2, pBoth, result
  Disp "P(C1 | C2) for Binomial(", n, ",", p, ")"
  pC2 := binomCdf(n, p, 0, c2)
  pBoth := binomCdf(n, p, 0, min(c1, c2))
  result := pBoth / pC2
  Disp "Result = ", approx(result)
EndPrgm


3. binominfo(n, p) — Binomial distribution information
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Define binominfo(n, p) = Prgm
  Local ev, var, sd, sev, ssd
  ev := n * p
  var := n * p * (1 - p)
  sd := sqrt(var)
  sev := p
  ssd := sqrt(p * (1 - p) / n)
  Disp "E(X) = ", ev
  Disp "Var(X) = ", var
  Disp "SD(X) = ", approx(sd)
  Disp "Sample E(p-hat) = ", sev
  Disp "Sample SD(p-hat) = ", approx(ssd)
EndPrgm


4. hypergeocdf(n, N, K, lo, hi) — Hypergeometric CDF
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Define hypergeocdf(n, bigN, bigK, lo, hi) = Prgm
  Local prob, i, p
  prob := 0
  For i, lo, hi
    p := nCr(bigK, i) * nCr(bigN - bigK, n - i) / nCr(bigN, n)
    prob := prob + p
  EndFor
  Disp "P(", lo, " <= X <= ", hi, ") = ", approx(prob)
EndPrgm


5. hypergeopdf(n, N, K, k) — Hypergeometric PMF
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Define hypergeopdf(n, bigN, bigK, k) = Prgm
  Local prob
  prob := nCr(bigK, k) * nCr(bigN - bigK, n - k) / nCr(bigN, n)
  Disp "P(X = ", k, ") = ", approx(prob)
EndPrgm


6. invbinomial(n, p, prob) — Inverse binomial
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Define invbinomial(n, p, prob) = Prgm
  Local k, cumprob
  k := 0
  cumprob := 0
  While cumprob < prob
    cumprob := cumprob + binomPdf(n, p, k)
    If cumprob >= prob Then
      Disp "k = ", k
      Disp "P(X <= ", k, ") = ", approx(cumprob)
      Return k
    EndIf
    k := k + 1
  EndWhile
EndPrgm


7. prtable(outcomes, probs) — Probability table statistics
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Define prtable(outcomes, probs) = Prgm
  Local ev, ex2, var, sd, i
  ev := 0
  ex2 := 0
  For i, 1, dim(outcomes)
    ev := ev + outcomes[i] * probs[i]
    ex2 := ex2 + outcomes[i]^2 * probs[i]
  EndFor
  var := ex2 - ev^2
  sd := sqrt(var)
  Disp "E(X) = ", ev
  Disp "E(X^2) = ", ex2
  Disp "Var(X) = ", var
  Disp "SD(X) = ", approx(sd)
EndPrgm


8. samplebinom(n, p) — Sample distribution for binomial
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Define samplebinom(n, p) = Prgm
  Local ev, sd
  ev := p
  sd := sqrt(p * (1 - p) / n)
  Disp "Sample proportion distribution:"
  Disp "E(p-hat) = ", ev
  Disp "SD(p-hat) = ", approx(sd)
  Disp "Approx Normal(", ev, ", ", approx(sd^2), ")"
EndPrgm


9. samplebinompr(n, p, lo, hi) — Sample binomial probability
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Define samplebinompr(n, p, lo, hi) = Prgm
  Local sd, result
  sd := sqrt(p * (1 - p) / n)
  result := normCdf(lo, hi, p, sd)
  Disp "P(", lo, " < p-hat < ", hi, ") = ", approx(result)
EndPrgm


10. samplehypergeo(n, N, K) — Sample hypergeometric distribution
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Define samplehypergeo(n, bigN, bigK) = Prgm
  Local p, ev, var, sd
  p := bigK / bigN
  ev := p
  var := (p * (1 - p) / n) * ((bigN - n) / (bigN - 1))
  sd := sqrt(var)
  Disp "p = K/N = ", approx(p)
  Disp "E(p-hat) = ", approx(ev)
  Disp "Var(p-hat) = ", approx(var)
  Disp "SD(p-hat) = ", approx(sd)
EndPrgm


11. samplehyppr(n, N, K, lo, hi) — Sample hypergeometric probability
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Define samplehyppr(n, bigN, bigK, lo, hi) = Prgm
  Local p, sd, fpc, result
  p := bigK / bigN
  fpc := sqrt((bigN - n) / (bigN - 1))
  sd := sqrt(p * (1 - p) / n) * fpc
  result := normCdf(lo, hi, p, sd)
  Disp "P(", lo, " < p-hat < ", hi, ") = ", approx(result)
EndPrgm