eQuate It CAS UDFs — Continuous Probability (TI-Nspire CAS)
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1. ccondpr — Continuous conditional probability
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(PDF version)
Define ccondpr(pdf, lo, hi) = Prgm
  Local pA, pAB
  Disp "P(lo < X < hi | condition)"
  pAB := ∫(pdf, x, lo, hi)
  Disp "P(A ∩ B) = ", pAB
EndPrgm

(Normal distribution version)
Define ccondpr(dummy, mu, sigma, c1, c2) = Prgm
  Local pC1, pC2, pBoth, result
  pC2 := normCdf(-∞, c2, mu, sigma)
  pC1 := normCdf(-∞, c1, mu, sigma)
  pBoth := normCdf(c1, c2, mu, sigma)
  If c1 < c2 Then
    result := pBoth / pC2
  Else
    result := pBoth / pC1
  EndIf
  Disp "P(condition1 | condition2) = ", approx(result)
EndPrgm


2. confint(n, phat, conf) — Confidence interval
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Define confint(n, phat, conf) = Prgm
  Local z, se, me, lo, hi
  z := invNorm((1 + conf)/2, 0, 1)
  se := sqrt(phat*(1 - phat)/n)
  me := z * se
  lo := phat - me
  hi := phat + me
  Disp "z-score: ", approx(z)
  Disp "Std error: ", approx(se)
  Disp "Margin of error: ", approx(me)
  Disp "CI: (", approx(lo), ", ", approx(hi), ")"
EndPrgm


3. confintsolve(lo, hi, unknown) — Solve for CI parameter
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Define confintsolve(lo, hi, unknown) = Prgm
  Local phat, me, z, se, n, conf
  phat := (lo + hi)/2
  me := (hi - lo)/2
  Disp "p-hat: ", approx(phat)
  Disp "Margin of error: ", approx(me)
  If string(unknown) = "n" Then
    Disp "Solving for sample size..."
    se := me / invNorm(0.975, 0, 1)
    n := ceiling(phat*(1 - phat)/se^2)
    Disp "n = ", n
  ElseIf string(unknown) = "conf" Then
    Disp "Solving for confidence level..."
  Else
    Disp "Unknown parameter: provide n, se, or conf"
  EndIf
EndPrgm


4. continfo(f, x, lo, hi) — Continuous distribution information
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Define continfo(f, x, lo, hi) = Prgm
  Local ev, var, sd
  ev := ∫(x*f, x, lo, hi)
  var := ∫(x^2*f, x, lo, hi) - ev^2
  sd := sqrt(var)
  Disp "E(X) = ", approx(ev)
  Disp "Var(X) = ", approx(var)
  Disp "SD(X) = ", approx(sd)
  Disp "Verification ∫f = ", approx(∫(f, x, lo, hi))
EndPrgm


5. invnormvals(mu, sigma, p) — Inverse normal (left, right, centre)
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Define invnormvals(mu, sigma, p) = Prgm
  Local left, right, clo, chi
  left := invNorm(p, mu, sigma)
  right := invNorm(1 - p, mu, sigma)
  clo := invNorm((1 - p)/2, mu, sigma)
  chi := invNorm((1 + p)/2, mu, sigma)
  Disp "P(X < a) = ", p
  Disp "  Left:   a = ", approx(left)
  Disp "P(X > a) = ", p
  Disp "  Right:  a = ", approx(right)
  Disp "P(lo < X < hi) = ", p
  Disp "  Centre: (", approx(clo), ", ", approx(chi), ")"
EndPrgm


6. normsolve — Solve for mu and sigma
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(Case 1: Both lower and upper given)
Define normsolve(lo, plo, hi, phi) = Prgm
  Local mu, sigma, result
  result := solve(normCdf(-∞, lo, mu, sigma) = plo and normCdf(-∞, hi, mu, sigma) = phi, {mu, sigma})
  Disp "mu = ", result[1]
  Disp "sigma = ", result[2]
EndPrgm