Changes

<div style="font-size:30px">'''PROB(xr,pr,ll,ul)'''</div><br/>

<div style="font-size:30px">'''PROB (Xs,Probabilities,lower_limit,upper_limit)

*<math>xr</math> is the array of x range of values in the function.

PROB(xr,pr,ll,ul)'''</div><br/>

*<math>pr</math> is the set of probabilities.

*<math>Xs</math> is the array of x range of values in the function.

*<math>ll</math> is the lower limit

*<math>Probabilities</math> is the set of probabilities.

*<math>ul</math> is the upper limit value.

*<math>lowerlimit</math> is the lower limit

*<math>upperlimit</math> is the upper limit value.

==Description==

==Description==

*Probability is the likelihood that an event will occur.  

*Probability is the likelihood that an event will occur.  

*Probabilities can be used to describe frequencies of outcomes in random experiments.

*Probabilities can be used to describe frequencies of outcomes in random experiments.

*In <math>PROB(xr,pr,ll,ul)</math>, <math>xr</math> is the array of numeric values which there are associated probabilities, <math>pr</math> is a set of probabilities associated with <math> xr</math>, <math>ll</math> is the lower limit of the probability and <math>ul</math> is the upper limit of the probability.

*In <math>PROB(Xs,Probabilities,lowerlimit,upperlimit)</math>, <math>Xs</math> is the array of numeric values which there are associated probabilities, <math>Probabilities</math> is a set of probabilities associated with <math> Xs</math>, <math>lowerlimit</math> is the lower limit of the probability and <math>upperlimit</math> is the upper limit of the probability.

*Here <math>ul</math> is optional. When we are omitting the value of <math>ul</math>, then the function simply returns the probability associated with the value of the given <math>ll</math>.

*Here <math>upperlimit</math> is optional. When we are omitting the value of <math>upperlimit</math>, then the function simply returns the probability associated with the value of the given <math>lowerlimit</math>.

*This function will return the result as error when  

*This function will return the result as error when  

  1.Any one of the value is non-numeric.

  1.Any one of the value is non-numeric.

  2.Any value of <math> pr \le 0 </math> or <math>pr >1</math>

  2.Any value of <math> Probabilities \le 0 </math> or <math>Probabilities >1</math>

  3.The values in the given <math>pr</math>  do not adding  up to 1

  3.The values in the given <math>Probabilities</math>  do not adding  up to 1

  4.<math>xr</math> and <math>pr</math> is of different number of data points.

  4.<math>Xs</math> and <math>Probabilities</math> is of different number of data points.

==Examples==

==Examples==