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Probability Density Functions
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08102016 01:04 AM  edited 08102016 04:22 AM
Hi,
Consider the following scenario:
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.
Can someone please show me how to use the my HP Prime Calculator to solve this problem?
Regards,
Arthur
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08102016 09:14 AM  edited 08102016 09:20 AM
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.
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.
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08102016 09:39 AM
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
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08102016 10:25 AM
¡ Hola !, @Athanasios:
See, this images ...
@Maké.
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08112016 04:03 PM
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.
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.
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08122016 02:49 AM
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
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08122016 10:58 AM
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.
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.
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08142016 06:54 PM  edited 08142016 07:02 PM
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.