<s> from sympy import ( EmptySet , FiniteSet , S , Symbol , Interval , exp , erf , sqrt , <EOL> symbols , simplify , Eq , cos , And , Tuple , integrate , oo , sin , Sum , Basic , <EOL> DiracDelta ) <EOL> from sympy . stats import ( Die , Normal , Exponential , P , E , variance , covariance , <EOL> skewness , density , given , independent , dependent , where , pspace , <EOL> random_symbols , sample ) <EOL> from sympy . stats . rv import ProductPSpace , rs_swap , Density , NamedArgsMixin <EOL> from sympy . utilities . pytest import raises , XFAIL <EOL> from sympy . core . compatibility import range <EOL> from sympy . abc import x <EOL> def test_where ( ) : <EOL> X , Y = Die ( '<STR_LIT:X>' ) , Die ( '<STR_LIT:Y>' ) <EOL> Z = Normal ( '<STR_LIT>' , <NUM_LIT:0> , <NUM_LIT:1> ) <EOL> assert where ( Z ** <NUM_LIT:2> <= <NUM_LIT:1> ) . set == Interval ( - <NUM_LIT:1> , <NUM_LIT:1> ) <EOL> assert where ( <EOL> Z ** <NUM_LIT:2> <= <NUM_LIT:1> ) . as_boolean ( ) == Interval ( - <NUM_LIT:1> , <NUM_LIT:1> ) . as_relational ( Z . symbol ) <EOL> assert where ( And ( X > Y , Y > <NUM_LIT:4> ) ) . as_boolean ( ) == And ( <EOL> Eq ( X . symbol , <NUM_LIT:6> ) , Eq ( Y . symbol , <NUM_LIT:5> ) ) <EOL> assert len ( where ( X < <NUM_LIT:3> ) . set ) == <NUM_LIT:2> <EOL> assert <NUM_LIT:1> in where ( X < <NUM_LIT:3> ) . set <EOL> X , Y = Normal ( '<STR_LIT:X>' , <NUM_LIT:0> , <NUM_LIT:1> ) , Normal ( '<STR_LIT:Y>' , <NUM_LIT:0> , <NUM_LIT:1> ) <EOL> assert where ( And ( X ** <NUM_LIT:2> <= <NUM_LIT:1> , X >= <NUM_LIT:0> ) ) . set == Interval ( <NUM_LIT:0> , <NUM_LIT:1> ) <EOL> XX = given ( X , And ( X ** <NUM_LIT:2> <= <NUM_LIT:1> , X >= <NUM_LIT:0> ) ) <EOL> assert XX . pspace . domain . set == Interval ( <NUM_LIT:0> , <NUM_LIT:1> ) <EOL> assert XX . pspace . domain . as_boolean ( ) == And ( <NUM_LIT:0> <= X . symbol , X . symbol ** <NUM_LIT:2> <= <NUM_LIT:1> , - oo < X . symbol , X . symbol < oo ) <EOL> with raises ( TypeError ) : <EOL> XX = given ( X , X + <NUM_LIT:3> ) <EOL> def test_random_symbols ( ) : <EOL> X , Y = Normal ( '<STR_LIT:X>' , <NUM_LIT:0> , <NUM_LIT:1> ) , Normal ( '<STR_LIT:Y>' , <NUM_LIT:0> , <NUM_LIT:1> ) <EOL> assert set ( random_symbols ( <NUM_LIT:2> * X + <NUM_LIT:1> ) ) == set ( ( X , ) ) <EOL> assert set ( random_symbols ( <NUM_LIT:2> * X + Y ) ) == set ( ( X , Y ) ) <EOL> assert set ( random_symbols ( <NUM_LIT:2> * X + Y . symbol ) ) == set ( ( X , ) ) <EOL> assert set ( random_symbols ( <NUM_LIT:2> ) ) == set ( ) <EOL> def test_pspace ( ) : <EOL> X , Y = Normal ( '<STR_LIT:X>' , <NUM_LIT:0> , <NUM_LIT:1> ) , Normal ( '<STR_LIT:Y>' , <NUM_LIT:0> , <NUM_LIT:1> ) <EOL> raises ( ValueError , lambda : pspace ( <NUM_LIT:5> + <NUM_LIT:3> ) ) <EOL> raises ( ValueError , lambda : pspace ( x < <NUM_LIT:1> ) ) <EOL> assert pspace ( X ) == X . pspace <EOL> assert pspace ( <NUM_LIT:2> * X + <NUM_LIT:1> ) == X . pspace <EOL> assert pspace ( <NUM_LIT:2> * X + Y ) == ProductPSpace ( Y . pspace , X . pspace ) <EOL> def test_rs_swap ( ) : <EOL> X = Normal ( '<STR_LIT:x>' , <NUM_LIT:0> , <NUM_LIT:1> ) <EOL> Y = Exponential ( '<STR_LIT:y>' , <NUM_LIT:1> ) <EOL> XX = Normal ( '<STR_LIT:x>' , <NUM_LIT:0> , <NUM_LIT:2> ) <EOL> YY = Normal ( '<STR_LIT:y>' , <NUM_LIT:0> , <NUM_LIT:3> ) <EOL> expr = <NUM_LIT:2> * X + Y <EOL> assert expr . subs ( rs_swap ( ( X , Y ) , ( YY , XX ) ) ) == <NUM_LIT:2> * XX + YY <EOL> def test_RandomSymbol ( ) : <EOL> X = Normal ( '<STR_LIT:x>' , <NUM_LIT:0> , <NUM_LIT:1> ) <EOL> Y = Normal ( '<STR_LIT:x>' , <NUM_LIT:0> , <NUM_LIT:2> ) <EOL> assert X . symbol == Y . symbol <EOL> assert X != Y <EOL> assert X . name == X . symbol . name <EOL> X = Normal ( '<STR_LIT>' , <NUM_LIT:0> , <NUM_LIT:1> ) <EOL> X = Normal ( '<STR_LIT>' , <NUM_LIT:0> , <NUM_LIT:1> ) <EOL> def test_RandomSymbol_diff ( ) : <EOL> X = Normal ( '<STR_LIT:x>' , <NUM_LIT:0> , <NUM_LIT:1> ) <EOL> assert ( <NUM_LIT:2> * X ) . diff ( X ) <EOL> def test_overlap ( ) : <EOL> X = Normal ( '<STR_LIT:x>' , <NUM_LIT:0> , <NUM_LIT:1> ) <EOL> Y = Normal ( '<STR_LIT:x>' , <NUM_LIT:0> , <NUM_LIT:2> ) <EOL> raises ( ValueError , lambda : P ( X > Y ) ) <EOL> def test_ProductPSpace ( ) : <EOL> X = Normal ( '<STR_LIT:X>' , <NUM_LIT:0> , <NUM_LIT:1> ) <EOL> Y = Normal ( '<STR_LIT:Y>' , <NUM_LIT:0> , <NUM_LIT:1> ) <EOL> px = X . pspace <EOL> py = Y . pspace <EOL> assert pspace ( X + Y ) == ProductPSpace ( px , py ) <EOL> assert pspace ( X + Y ) == ProductPSpace ( py , px ) <EOL> def test_E ( ) : <EOL> assert E ( <NUM_LIT:5> ) == <NUM_LIT:5> <EOL> def test_Sample ( ) : <EOL> X = Die ( '<STR_LIT:X>' , <NUM_LIT:6> ) <EOL> Y = Normal ( '<STR_LIT:Y>' , <NUM_LIT:0> , <NUM_LIT:1> ) <EOL> z = Symbol ( '<STR_LIT:z>' ) <EOL> assert sample ( X ) in [ <NUM_LIT:1> , <NUM_LIT:2> , <NUM_LIT:3> , <NUM_LIT:4> , <NUM_LIT:5> , <NUM_LIT:6> ] <EOL> assert sample ( X + Y ) . is_Float <EOL> P ( X + Y > <NUM_LIT:0> , Y < <NUM_LIT:0> , numsamples = <NUM_LIT:10> ) . is_number <EOL> assert E ( X + Y , numsamples = <NUM_LIT:10> ) . is_number <EOL> assert variance ( X + Y , numsamples = <NUM_LIT:10> ) . is_number <EOL> raises ( ValueError , lambda : P ( Y > z , numsamples = <NUM_LIT:5> ) ) <EOL> assert P ( sin ( Y ) <= <NUM_LIT:1> , numsamples = <NUM_LIT:10> ) == <NUM_LIT:1> <EOL> assert P ( sin ( Y ) <= <NUM_LIT:1> , cos ( Y ) < <NUM_LIT:1> , numsamples = <NUM_LIT:10> ) == <NUM_LIT:1> <EOL> E ( Sum ( <NUM_LIT:1> / z ** Y , ( z , <NUM_LIT:1> , oo ) ) , Y > <NUM_LIT:2> , numsamples = <NUM_LIT:3> ) <EOL> assert all ( i in range ( <NUM_LIT:1> , <NUM_LIT:7> ) for i in density ( X , numsamples = <NUM_LIT:10> ) ) <EOL> assert all ( i in range ( <NUM_LIT:4> , <NUM_LIT:7> ) for i in density ( X , X > <NUM_LIT:3> , numsamples = <NUM_LIT:10> ) ) <EOL> def test_given ( ) : <EOL> X = Normal ( '<STR_LIT:X>' , <NUM_LIT:0> , <NUM_LIT:1> ) <EOL> Y = Normal ( '<STR_LIT:Y>' , <NUM_LIT:0> , <NUM_LIT:1> ) <EOL> A = given ( X , True ) <EOL> B = given ( X , Y > <NUM_LIT:2> ) <EOL> assert X == A == B <EOL> def test_dependence ( ) : <EOL> X , Y = Die ( '<STR_LIT:X>' ) , Die ( '<STR_LIT:Y>' ) <EOL> assert independent ( X , <NUM_LIT:2> * Y ) <EOL> assert not dependent ( X , <NUM_LIT:2> * Y ) <EOL> X , Y = Normal ( '<STR_LIT:X>' , <NUM_LIT:0> , <NUM_LIT:1> ) , Normal ( '<STR_LIT:Y>' , <NUM_LIT:0> , <NUM_LIT:1> ) <EOL> assert independent ( X , Y ) <EOL> assert dependent ( X , <NUM_LIT:2> * X ) <EOL> XX , YY = given ( Tuple ( X , Y ) , Eq ( X + Y , <NUM_LIT:3> ) ) <EOL> assert dependent ( XX , YY ) <EOL> @ XFAIL <EOL> def test_dependent_finite ( ) : <EOL> X , Y = Die ( '<STR_LIT:X>' ) , Die ( '<STR_LIT:Y>' ) <EOL> assert dependent ( X , Y + X ) <EOL> XX , YY = given ( Tuple ( X , Y ) , X + Y > <NUM_LIT:5> ) <EOL> assert dependent ( XX , YY ) <EOL> def test_normality ( ) : <EOL> X , Y = Normal ( '<STR_LIT:X>' , <NUM_LIT:0> , <NUM_LIT:1> ) , Normal ( '<STR_LIT:Y>' , <NUM_LIT:0> , <NUM_LIT:1> ) <EOL> x , z = symbols ( '<STR_LIT>' , real = True , finite = True ) <EOL> dens = density ( X - Y , Eq ( X + Y , z ) ) <EOL> assert integrate ( dens ( x ) , ( x , - oo , oo ) ) == <NUM_LIT:1> <EOL> def test_Density ( ) : <EOL> X = Die ( '<STR_LIT:X>' , <NUM_LIT:6> ) <EOL> d = Density ( X ) <EOL> assert d . doit ( ) == density ( X ) <EOL> def test_NamedArgsMixin ( ) : <EOL> class Foo ( Basic , NamedArgsMixin ) : <EOL> _argnames = '<STR_LIT:foo>' , '<STR_LIT:bar>' <EOL> a = Foo ( <NUM_LIT:1> , <NUM_LIT:2> ) <EOL> assert a . foo == <NUM_LIT:1> <EOL> assert a . bar == <NUM_LIT:2> <EOL> raises ( AttributeError , lambda : a . baz ) <EOL> class Bar ( Basic , NamedArgsMixin ) : <EOL> pass <EOL> raises ( AttributeError , lambda : Bar ( <NUM_LIT:1> , <NUM_LIT:2> ) . foo ) <EOL> def test_density_constant ( ) : <EOL> assert density ( <NUM_LIT:3> ) ( <NUM_LIT:2> ) == <NUM_LIT:0> <EOL> assert density ( <NUM_LIT:3> ) ( <NUM_LIT:3> ) == DiracDelta ( <NUM_LIT:0> ) <EOL> def test_real ( ) : <EOL> x = Normal ( '<STR_LIT:x>' , <NUM_LIT:0> , <NUM_LIT:1> ) <EOL> assert x . is_real <EOL> def test_issue_10052 ( ) : <EOL> X = Exponential ( '<STR_LIT:X>' , <NUM_LIT:3> ) <EOL> assert P ( X < oo ) == <NUM_LIT:1> <EOL> assert P ( X > oo ) == <NUM_LIT:0> <EOL> assert P ( X < <NUM_LIT:2> , X > oo ) == <NUM_LIT:0> <EOL> assert P ( X < oo , X > oo ) == <NUM_LIT:0> <EOL> assert P ( X < oo , X > <NUM_LIT:2> ) == <NUM_LIT:1> <EOL> assert P ( X < <NUM_LIT:3> , X == <NUM_LIT:2> ) == <NUM_LIT:0> <EOL> raises ( ValueError , lambda : P ( <NUM_LIT:1> ) ) <EOL> raises ( ValueError , lambda : P ( X < <NUM_LIT:1> , <NUM_LIT:2> ) ) </s>
