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Intern
Posts: 44
Member Since: ‎05-25-2015
Message 1 of 8 (986 Views)

Probability Density Functions

[ Edited ]

Hi,

 

Consider the following scenario:

 

10-08-2016 4-56-50 PM.jpg

 

The above scenario is a calculator question. I am able to complete it by hand but I would like to know how to use CAS technology. When I attempt to solve the question using the HP Prime Calculator I am unable to do so.

 10-08-2016 5-00-35 PM.jpg

 

10-08-2016 5-00-57 PM.jpg

 

10-08-2016 5-02-13 PM.jpg

 

 

 

 

Can someone please show me how to use the my HP Prime Calculator to solve this problem?

 

Regards,

Arthur

 

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PhD Student
Posts: 601
Member Since: ‎01-08-2009
Message 2 of 8 (949 Views)

Re: Probability Density Functions

[ Edited ]

Hello,

 

I'm fairly certain the problem is a missing space between your x and =.25 This causes it to associate the =.25 with the x, and not the whole integral. What you have in essence entered is (...cos(x)d(x=.25)) instead of (...cos(x)dx) = .25 . Hence why it complains about "not being an equation". Indeed, in your second example it shows in the location for the variable on integrand an int(cos(2*x),x=.25,3*pi/4,a) when it should be int(cos(2*x),x,3*pi/4,a)=.25 - the whole inegral equal to 1/4.

 

I was using the integral template to enter the input. To access that, press the "template" key which is the one just to the left of the toolbox. When you enter the dx part, press one more space to move outside the integral template, and type the =.25

 

With that space after the dx<space> and I think it will work for you fine. Also note that if you want exact results, you should not put any approximate decimal values in your input. Note the second one how I used 1/4 and get the exact, symbolic answers.

 

screen.png

TW

Although I work for the HP calculator group as a head developer of the HP Prime, the views and opinions I post here are my own.
Teacher
Posts: 49
Member Since: ‎10-21-2014
Message 3 of 8 (947 Views)

Re: Probability Density Functions

Hello Arthur,

 

I haven't a Prime, but with my Hp 50g I solve such problems with the ROOT command:

 

ROOT('Int(3*pi/4,A,COS(2*X),X) - 0.25 = 0','A',3.141)

 

First value = Expr

Second value = Variable

Third value = initial guess

 

Int stands for the integral sign

 

Maybe that helps. C is correct, my HP 50g find the solution in 5 seconds.

 

Regards calcpeace

Distinguished Professor
Posts: 2,795
Member Since: ‎02-17-2015
Message 4 of 8 (940 Views)

Re: Probability Density Functions

¡ Hola !, @Athanasios:

 

See, this images ...

IMG_20160810_132101.jpg

IMG_20160810_132141.jpg

Kind Regards.
@Maké.
PhD Student
Posts: 601
Member Since: ‎01-08-2009
Message 5 of 8 (902 Views)

Re: Probability Density Functions

Yes, it solves instantly on Prime as well. The problem is basically this in essence:

 

ROOT('Int(3*pi/4,A,COS(2*X),X- 0.25 ) = 0','A',3.141)

 

The variable of integration has =.25 in the argument position.

TW

Although I work for the HP calculator group as a head developer of the HP Prime, the views and opinions I post here are my own.
Teacher
Posts: 49
Member Since: ‎10-21-2014
Message 6 of 8 (890 Views)

Re: Probability Density Functions

Hello Tim,

 

My Version:

"ROOT('Int(3*pi/4,A,COS(2*X),X) - 0.25  = 0','A',3.141)"

                                                            ^

 

Your Version:

"ROOT('Int(3*pi/4,A,COS(2*X),X- 0.25 ) = 0','A',3.141)

                                                                         ^

The variable of integration has =.25 in the argument position."

 

I don't understand your modifikation. You transform x -> x - 0.25.

In my opinion is 0.25 the aera, it is value you get after the integration.

I even get a error message inputting your version (in the HP 50g), because the fourth argument is only allowed to be a variable name  for the integral function .

Or I'm going a wrong way?

 

Regards calcpeace

PhD Student
Posts: 601
Member Since: ‎01-08-2009
Message 7 of 8 (870 Views)

Re: Probability Density Functions

 


calcpeace wrote:

 

 

I don't understand your modifikation. You transform x -> x - 0.25.

In my opinion is 0.25 the aera, it is value you get after the integration.

I even get a error message inputting your version (in the HP 50g), because the fourth argument is only allowed to be a variable name  for the integral function .

Or I'm going a wrong way?

 

Regards calcpeace


Exactly. That is the problem here I was trying to show. The argument for variable of integration isn't a variable in the OP's input but rather an X=.25 which as you point out causes an error in the 50g as well.

TW

Although I work for the HP calculator group as a head developer of the HP Prime, the views and opinions I post here are my own.
Teacher
Posts: 125
Member Since: ‎04-03-2015
Message 8 of 8 (801 Views)

Re: Probability Density Functions

[ Edited ]

I find it easier to just place the 0.25 in front of the int() to avoid any spacing issues:  solve(0.25 = int(cos(2*x),x,3/4*π,a),a)

 

Also, to automatically convert to 0.25 to a fraction, highlight the solve(...) in history and press the [a b/c] key.  The answer will contain fractions automatically.  Tap twice on the result to copy to the entry line and press [Enter] to get the exact result.

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