+
    i                     r   ^ RI Ht ^ RIHt ^ RIHt ^ RIHtHtH	t	 ^ RI
Ht ^ RIHtHt ^ RIHtHtHt ^ RIHt ^ R	IHt ^ R
IHt ^ RIHt ^ RIHt ^ RIHt ^ RIH t  ^ RI!H"t" ^ RI#H$t$H%t% ^ RIH&t& ^ RI'H(t(H)t)H*t*H+t+H,t,H-t- ^ RI.H/t/ ^ RI0H1t1 ^ RI2H3t3H4t4 ^ RI5H6t6 ^ RI7H8t8H9t9 ^ RI:H;t; R t<R t=R t>R t?R# )    )Sum)Add)Mul)Integeroopi)Pow)EqNe)DummySymbolsymbols)	factorial)exp)sqrt)	Piecewise)
DiracDelta)gamma)Integral)simplify)IndexedIndexedBase)ExprCondPair)PoissonBetaExponentialPMultinomialMultivariateBeta)Normal)PoissonDistribution)CompoundPSpaceCompoundDistribution)MarginalDistribution)pspacedensity)ignore_warningsc            	         \        R 4      p \        RRR7      p\        V^^4      p\        W4      p\        \	        V4      \
        4      '       g   Q h\        V\        W"P                  4      4      \        V4      8X  g   Q h\        R^ ^4      p\        RV^4      p\        V4      ! ^ 4      P                  4       \        ^
4      ^
\        \        4      ,          ,          8X  g   Q h\        \        V\        V^4      4      ! V 4      4      \        ^4      \        V ^,
          ^,          ) ^,          4      ,          ^\        \        4      ,          ,          8X  g   Q h\        \        V4      ! V 4      4      \        ^
4      \        V ^,          ) ^
,          4      ,          ^
\        \        4      ,          ,          8X  g   Q hR# )xlTpositiveN1N2N)r   r   r   
isinstancer%   r"   r&   r
   symbolr!   r    doitr   r   r   r   )r)   r*   rateXr-   r.   s         X/var/www/html/photoedit/myenv/lib/python3.14/site-packages/sympy/stats/tests/test_mix.pytest_densityr5      sI   sAsT"A1a=DAfQi00001b{{+,0CA0FFFF	a	B	b!	B2;q> DHbbk$::::GB2q	*1-.Qa!eaZKM""Ad2hJ/0 0 0GBKN#tBxQTE"H'=r$r({'KKKK    c                     \        R RR7      w  rp\        R^W4      p\        RW^ ,          4      p\        WC^ ,          34      p\	        \        R4      \        \        \	        \        ^4      \        \        RRR7      \        \        \        R4      4      \        ^ 4      4      4      \        \        RRR7      \        \        \        R4      4      \        ^4      4      4      \        \        \        \        \        R4      4      \        ^ 4      4      4      \        R	4      4      \        \        \        \        \        R4      4      \        ^4      4      4      \        R	4      4      4      \        \        \        \        \        R4      4      \        ^ 4      4      \        \        \        R4      4      \        ^4      4      4      \        ^4      4      4      \        \        ^ 4      R4      4      \        \        \        RRR7      4      \        R	4      4      \        \        \        RRR7      \        \        \        R4      4      \        ^ 4      4      4      4      \        \        \        \        \        R4      4      \        ^ 4      4      4      \        R	4      4      \        \        \        \        R4      4      \        ^ 4      4      \        \        RRR7      \        R	4      4      4      \        \        \        \        R4      4      \        ^4      4      \        \        \        \        R4      4      \        ^ 4      4      \        R	4      4      4      4      pV! V4      V8X  g   Q hR# )
za1 p1 p2Tr+   CBp1p2a1N)r   r   r   r$   r   r   r   r   r   r	   r   r   r   r
   r   r   )r<   r:   r;   r8   r9   MGRmgrcs          r4   test_MarginalDistributionr@   )   s_   d3JBBCB#AbA$'A
qQ4'
*Cvc{Il3wqztd#W[-EAJ& fTD1Ks$gaj13	'+fSk2GAJ?@'"+N	'+fSk2GAJ?@'"+N4P s7;vc{+WQZ8Ks$gaj134;AJ@'A T"$ &)vdT/J)KBK&F4$7Ks$gaj13 4gk&+.
;<gbkJF3K('!*5td#WR[13F3K('!*5F3K('!*5wr{CEFD  q6T>>r6   c                     \        R ^4      p \        RV 4      p\        \        V4      \        4      '       g   Q h\        \        V4      P                  \
        4      '       g   Q hVP                  P                  P                  ^4      P                  4       \        R4      \        \        R4      4      ,          8X  g   Q hR# )YZNr=   )	r   r/   r%   r"   distributionr#   pdfr1   r   )rB   rC   s     r4   test_compound_distributionrG   @   s    QAQAfQi0000fQi,,.BCCCC88  $$Q',,.#b'#c"g,2FFFFr6   c                     \        R ^4      \        R^4      r\        R4      p\        \	        \        R4      \        \        V) 4      \        V^,
          4      ,          V^ \        34      ,          \        V4      ,          V^ \        34      V\        ) ^ 34      p\        \	        \        R4      \        \        V) 4      \        V^,
          4      ,          V^ \        34      ,          \        V4      ,          V^ \        34      V^ \        34      p\        \        W,           ^4      4      ^ 8X  g   Q h\        \        W,           ^4      4      ^8X  g   Q h\        \        4      ;_uu_ 4        \        W,           ^8  RR7      P                  \        4      P                  V4      '       g   Q h\        W,           ^8  RR7      P                  \        4      P                  V4      '       g   Q h RRR4       R#   + '       g   i     R# ; i)rB   EkF)evaluateNr=   )r   r   r   r   r   r   r   r   r   r   r
   r   r'   UserWarningrewritedummy_eq)rB   rI   rJ   expr1expr2s        r4   test_mix_expressionrQ   G   s   3?KQ/qc
ASR#qb'*QU2C*CaBZ " l2J "#bS!.ESR#qb'*QU2C*CaBZ " l2J "#Q-ERq\?aRq\?a		%	%U+33H=FFuMMMMU+33H=FFuMMMM 
&	%	%	%s   +BG77H	N)@sympy.concrete.summationsr   sympy.core.addr   sympy.core.mulr   sympy.core.numbersr   r   r   sympy.core.powerr	   sympy.core.relationalr
   r   sympy.core.symbolr   r   r   (sympy.functions.combinatorial.factorialsr   &sympy.functions.elementary.exponentialr   (sympy.functions.elementary.miscellaneousr   $sympy.functions.elementary.piecewiser   'sympy.functions.special.delta_functionsr   'sympy.functions.special.gamma_functionsr   sympy.integrals.integralsr   sympy.simplify.simplifyr   sympy.tensor.indexedr   r   r   sympy.statsr   r   r   r   r   r   sympy.stats.crv_typesr    sympy.stats.drv_typesr!   sympy.stats.compound_rvr"   r#   sympy.stats.joint_rvr$   sympy.stats.rvr%   r&   sympy.testing.pytestr'   r5   r@   rG   rQ    r6   r4   <module>rj      sq    )   0 0   * 6 6 > 6 9 : > 9 . , 7 =7 7 ( 5 H 5 * 0L.GNr6   