Probability Density Function:

Learning probability density functions:

In a normal distribution, curve quantity is y, which is represented the height f the curve at any point along x axis is called Probability density function. Here the probability density function represented using the intervals. The probability density function denoted by f(x) this function is also known as the probability distribution function and mass function, it will be referred as the probability density function(pdf).

Learning of probability density functions helps to know about the density functions of probability. The learning of the these functions are usually done in higher level of education. Learning the function of Probability density is easy when the concept is understood very clearly.

Learning Probability Density Function:

The probability of a random variable declining within a certain set is given by the integral of its density over the set. The continuous random variable is a x, and then the probability density function of x is a f(x) such that for two numbers a and b with a b

Probability distribution function is used to denote the probability density function. It may refer to the cumulative distribution function, or it may be a probability mass function rather than the density.

Formula:

A random variable which has a usual distribution with a mean m=0 and a standard deviation σ=1 is referred to as Standard Normal Distribution.

Normal Distribution = P(x) = (1/ (σ √(2π))) e^{-(x-m)2 / (2σ2)}

Standard Normal Distribution = P(x) = (1/√(2π)) e^{-(x2 / 2)}

Here m = mean σ is standard deviation, = 3.14 e= 2.718.

The normal distribution, also recognized as the Gaussian distribution, is the most widely-used common purpose distribution. It is for this reason that it is included among the lifetime distributions generally used for reliability and life data analysis.

How to Find Probability Density Function:

Solve: mean m=5

Standard deviation σ=4
Normal random variable x=6 find the probability function

Solution:

• Step 1: To calculate PDF find sqrt (2π).

sqrt (2π) = sqrt (2 x 3.14)

= sqrt (6.28) = 2.51

• Step 2: Find 1/ (σsqrt (2π)).

σsqrt (2π) = 4 x 2.51 = 10.04
1/(σsqrt(2π)) = 1/10.04 = 0.099

• Step 3: To Find e^{-(x-m) 2 / (2σ2)} and calculate -(x-m) ² and 2σ².

-(x-m) ² = - (6-5)²
= 1² = 1
2σ² = 2 x (4²)
= 2 x 16 = 32
-(x-m) ² / (2σ²) = 1/32
= 0.03125

• Step 4: Calculate e^{-(x-m) 2 / (2σ2)}

= 2.718^0.03125

= 1.0317

• Step 5: To find PDF formula is used.

= 0.099 x 1.0317

= 0.1021

Hope you like the above example of Probability Density Function.Please leave your comments, if you have any doubts.