Probability Function : What is difference between cumulative distribution function & Probability mass function. Need help with understanding TRUE/FALSE option of NORMDIST excel function.

Example : For one given value, (Value/Mean /Std.Dev/(TRUE/FALSE )) the output was .908 & .109. Help appreciated...

Dear Kiran,

We need to differentiate between continuous and discrete variables.

Let's first look at the discrete case. For example, if we are talking about tossing a coin. The probability of getting a head is 0.5 and the probability of getting a tail is 0.5. The value 0.5 can be referred to as the probability mass function.

For continuous variables, the probability mass function is referred to as the probability density function. However, the value of the probability density function does not equal the probability of getting a value in the continuous case. In fact, the probability of exactly getting a value for a continuous distribution is always 0.

The area under the probability density function gives the probability in the continuous case. For example, if we have normally distributed data with mean = 20 and standard deviation = 5, then the probability of getting say 20, P(20) = 0. We can however, calculate the probability of getting values between 19 and 21, represented as P(19 < X < 21).

If we look at the probability of getting all values less than 21, i.e. P(X < 21), this function is called the cumulative distribution function. It is the area to the left of that value under the probability density function. This can also be represented as CDF(21).

Note: P(19 < X < 21) = CDF(21) - CDF(19). The area between 19 and 21 is equal to the total area to the left of 21 minus the total area to the left of 19.

In most cases, for continuous distributions, we usually work with areas, so CDF values are more important than PDF. However, when we plot the distribution functions, we usually plot the PDF as their shapes are easier to recognize compared to CDF.

It is hard to explain this without a figure. Hope this helps.

SJ.

hi i m still confuse with both terms i.e PDF & CDF.

Dear Rajesh, 

If you toss twenty coins, PDF can tell you the probability of getting exactly 10 heads. CDF shall provide you the probability of getting up to 10 heads (This is the cumulative of getting 0,1,2,3 ......10 heads)

In a similar way, CDF can provide you the probability of obtaining a PIZZA within 30 minutes if you know the mean and standard deviation of normally distributed PIZZA delivery data. 

If you need statistical details, have a look here

Have a look at this one. CDF is ever increasing till it reaches 100% as it is the cumulative distribution. PDF can have  peaks as it shows actual probability. We can derive PDF from CDF and vice versa. 

http://www.predictionprobe.com/DistributionProbe/ex1_PDF_CDF.jpg