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May 11th, 2014, 06:07 AM  #1 
Newbie Joined: Apr 2014 From: Manama, Bahrain Posts: 18 Thanks: 1 Math Focus: Probability and Statistics :P  Question about Probability Density Functions
Hello everyone (: Can somebody please explain this to me? ЁЯСЙ In a continuous probability distribution, why is P(X = x) = 0? i.e., why is the probability that the continuous random variable, X, takes a discrete value, x (say, x = 1) equal to 0? Why can the PDF only be used to calculate the probability of a continuous RV take a value less than OR greater than but NOT equal to a certain discrete value? For eg. : Consider the (continuous) probability distribution of the heights of 20 individuals. According to what I've learnt, the probability that the height of a randomly selected individual out of those 20 individuals is, say 180cm = 0. How is that possible? Cos, 180cm seem to be a likely possibility/outcome intuitively; so why does probability theory prove otherwise? Thank you for the help (: 
May 11th, 2014, 09:28 AM  #2 
Math Team Joined: Jul 2013 From: рдХрд╛рдардорд╛рдбреМрдВ, рдиреЗрдкрд╛рд▓ Posts: 879 Thanks: 60 Math Focus: рд╕рд╛рдорд╛рдиреНрдп рдЧрдгрд┐рдд 
continuous probability distribution is a distrubution for a random variable which takes continuous value (anologue type of value). Example : there are infinite numbers between 0 and 1. Like 0.01, 0.0068, 0.563234 etc. this is true for any two numbers a and b. If a random variable is to take any one value between a and b it can assume value among those infinite number of values. This kind of probability bistribution cannot be represented in discrete points so continuous distribution is used. A continuous random variable cannot take a fixed value like X = 0 because the probability for the RV to take the value is 0 Example : there are infinite number of points between two numbers a and b among which c may be one. the probability that the RV may take the value c P(X=c) = number of c / total number of possible points = 1 / infinity = 0 
May 11th, 2014, 02:19 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,683 Thanks: 658 
180 cm is a likely possibility as an approximation, but not exact, i.e. 180.0000000000...... has probability 0. 
May 11th, 2014, 10:53 PM  #4  
Newbie Joined: Apr 2014 From: Manama, Bahrain Posts: 18 Thanks: 1 Math Focus: Probability and Statistics :P  Quote:
Oh alright; so it's just that if you substitute x = 180 in the PDF of the concerned continuous distribution, you will get some probability value but if you substitute x = 180 in the PMF of the distribution you get 0 (since P(X = x) = 0 for continuous RV distributions). Thank you (:  

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