Advanced Search

Question: Trouble with the PDF Function

Question:Trouble with the PDF Function

JoyDivisionMan 70 Maple 2025
statistics
9 hours ago
0

I have created three random variables:  r, theta and phi.  That went as I expected.  I then did some math with these random variable.  I calculated the following:  sin(phi), sin(theta), cos(phi) and cos(theta).

When I viewed the PDFs of these above four, I get what I expected with the exception of sin(theta).  I got an error message telling me that I provided three arguments when Maple expected only two arguments.  I am confused as to why this happened.

I wonder if I broke any rules when I named these variables, but I don't know...any suggestions? My work is attached.

> 

with(Statistics)
> 

theta := RandomVariable(Uniform(0, 2*Pi))

_R

 (1)
> 

phi := arccos(-1+2*RandomVariable(Uniform(0, 1)))

arccos(-1+2*_R0)

 (2)
> 

r := RandomVariable(Uniform(0, 1))^(1/3)

_R1^(1/3)

 (3)
> 

SinPhi := sin(phi)

2*(-_R0^2+_R0)^(1/2)

 (4)
> 

PDF(SinPhi, t)

piecewise(t <= 0, 0, t < (1/2)*4^(1/2), t/(-t^2+1)^(1/2), (1/2)*4^(1/2) <= t, 0)

 (5)
> 

SinTheta := sin(theta)

sin(_R)

 (6)
> 

PDF(SinTheta, t)

Error, (in Statistics:-PDF) invalid input: type expects 2 arguments, but received 3

  
> 

CosPhi := cos(phi)

-1+2*_R0

 (7)
> 

PDF(CosPhi, t)

(1/2)*piecewise((1/2)*t < -1/2, 0, (1/2)*t < 1/2, 1, 0)

 (8)
> 

CosTheta := cos(theta)

cos(_R)

 (9)
> 

PDF(CosTheta, t)

piecewise(t <= -1, 0, t < 1, 1/(Pi*(-t^2+1)^(1/2)), 1 <= t, 0)

 (10)
 

NULL

Download Basics.mw
Please Wait...