Difference between normal distribution and probability density function
Answers
Answer:
Probability density function: for a continuous random variable X, we can define the probability that X is in [a,b] as
P(a<=X<=b)=\int_a^b f(x) dx. (integral)
Where f(x) is probability density function, which satisfies two properties
f(x)>=0 and \int_{-infinity}^{+infinity}f(x) dx =1. a, b are real numbers.
Probability distribution function defines the probability that X<=a as
P(X<=a)=\int_{-infinity}^a f(x) dx
It is important to say that probability distribution function is a probability (I.e., its value is a number between 0 and one), and it is defined for both discrete and continuous random variables. Probability density function contains information about probability but it is not a probability since can have any value positive, even larger than one. It is defined only for continuous random variables; for discrete random variables the probability mass function can be defined (as mentioned by Philipp), which is a probability, P(X=a).