Density Function | Statistics
Download as PPT, PDF1 like2,664 views
The document explains the concept of probability density functions for continuous random variables, comparing them to distribution functions for discrete variables. It provides examples, such as a binomial probability distribution and the normal distribution, illustrating how density functions can represent the probability of events occurring within a certain range. A practical example is given regarding client appointment times between noon and 2 PM to demonstrate how to calculate probabilities using density functions.
Density Function | Statistics
- 2. Density FunctionDensity Function Density Function, for discrete variable is similar to distribution function It can be considered as a “smoothed” distribution function Let us suppose ‘X’ to be a continuous random variable. And x be the value that variable X takes. In such case f(x) is used to describe density function
- 3. x0 ba Probability Density Function shows that the probability of the random variable lies in a particular range. f(x)
- 4. Probability DistributionProbability Distribution Function (for discreteFunction (for discrete variable) Vs Probabilityvariable) Vs Probability density function (fordensity function (for continuous variable)continuous variable) Binimial probability Dis tribution func tio n with s uc c e s s pro b 0.5 and total # trial 50 0 0.02 0.04 0.06 0.08 0.1 0.12 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 Probability Dins ity Func tion Example (Normal Dis tribution with me an 25 and SD 3.2) 0 0.02 0.04 0.06 0.08 0.1 0.12 0 5 10 15 20 25 30 35 40 45 50
- 5. Density Function: ExampleDensity Function: Example Suppose your client confirms an appointment between noon and 2pm. Here, the time of arrival is absolutely random. Let, X = the random variable for arrival time (X=1.5 means he visit your office at 1:30pm) And, x be the possible value, random variable X can take.
- 6. ExampleExample 0 2 0.5 x f(x) Then, density function f(x) will be
- 7. Probability Density FunctionProbability Density Function ExampleExample 0 2 0.5 x f(x) 0.5 1 The probability that your client visits your office between 12:30 and 1:00 is given by the shaded area.
- 8. Probability Density FunctionProbability Density Function ExampleExample 0 2 0.5 x f(x) Note that area between 0 and 2 should be equal to 1 since the probability that your clients arrives between noon and 2pm is 1 (assuming that he will keep his promise that he will visit between noon and 2pm)
- 9. Density Function :NormalDensity Function :Normal DistributionDistribution xµ 0.0 0.1 0.2 0.3 0.4
- 10. Hey Friend, This was just a summary on Density Function. For more detailed information on this topic, please type the link given below or copy it from the description of this PPT and open it in a new browser window. www.transtutors.com/homework-help/statistics/density- function.aspx