How can write the following ? where p is probability ?

Answer 1

[Star Strider]

The ‘Z’ variable implies that the probability is normally distributed, so to calculate the probability, either use the normcdf function, or if you don’t have it, this anonymous function that does the same calculation:

P = @(z) erfc(-z/sqrt(2))/2;                  % Equivalent to ‘normcdf’

I am making some assumptions here. I need to know more about what you are doing to be certain the function is normally distributed.

[mohammed elmenshawy]

x is random variable follow the truncated normal distribution . i want calculate the probability p(x<-0.5271) and p(x>0.02) ?

[Walter Roberson]

The probability might be 0 if you truncated to (say) +/- 0.1

When you do the truncation, where does the extra unused probability go? Is the probability that would normally correspond to values more extreme than the limit all to be assigned to the exact value of the limit, leading to a non-differentiable spike at the limit?

The sum is over only 1 and 2,and at both of those the right hand side of the comparison is negative, because the 2 to the 2*i will always be greater than 1 over that range, and the multiplier constant is negative. It is not obvious why you would then be wanting to ask about the probability associated with a positive value

[Star Strider]

You can easily write you own code to calculate the truncated normal distribution, or you can use the function in TRUNCATED_NORMAL - The Truncated Normal Distribution.

EDIT — A thorough discussion of it is at The Truncated Normal Distribution.