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 December 4th, 2012, 07:00 PM #1 Newbie   Joined: Dec 2012 Posts: 4 Thanks: 0 probability at a point for a continuous random variable Hello all, I am new to this forum, and also to the field of random variables. I have a doubt regarding the existence of the probability that a continuous random variable x to take a particular value X. I read that, this probability is equal to 0, which was proved by considering the probability, P(X-e0, the LHS becomes P(x=X) , and RHS, goes to zero, as the left limit Lt(e->0) F(X-e) = F(X). But i cant interpret this result. Wont the probability density function p(x) at the point x=X, give the probability that x takes the value X? Why would this be equal to 0?. Plz help me out... December 5th, 2012, 12:24 PM #2 Global Moderator   Joined: May 2007 Posts: 6,822 Thanks: 723 Re: probability at a point for a continuous random variable Probability density function is the derivative of the probability distribution function. Unless the distribution has a jump at a particular point, the probability of that point = 0. January 7th, 2013, 02:27 AM #3 Newbie   Joined: Dec 2012 Posts: 4 Thanks: 0 Re: probability at a point for a continuous random variable Hello mathman, thanks for the reply... Is the definition of density function is : the probability that the random variable takes the value? In that case, i dont understand why the probability a random variable takes a particular value is zero? Or is my definition of density function wrong ? Kindly help me out... January 7th, 2013, 03:25 PM   #4
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Re: probability at a point for a continuous random variable

Quote:
 Originally Posted by rsashwinkumar Hello mathman, thanks for the reply... Is the definition of density function is : the probability that the random variable takes the value? In that case, i dont understand why the probability a random variable takes a particular value is zero? Or is my definition of density function wrong ? Kindly help me out...
The best way to look at probability is in terms of a distribution function, say F(x). (For simplicity, I will take the case where there are F(x) is continuous.) The probability that the random variable is in an interval (a,b) is F(b) - F(a). Here the probability at a point c = F(c) - F(c) = 0. The probability density is the derivative of F(x) and should not be interpreted a a probability.

The only case where probability is non-zero at a point is where F(x) has a jump at that point and the probability is the value of the jump. Tags continuous, point, probability, random, variable Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post lawochekel Algebra 1 April 19th, 2012 12:39 PM fin0c Advanced Statistics 1 January 23rd, 2011 10:43 PM meph1st0pheles Advanced Statistics 0 February 22nd, 2010 06:27 PM codedzero Advanced Statistics 1 August 30th, 2009 03:15 PM babyRudin Real Analysis 6 October 24th, 2008 12:58 AM

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