1. 教育部網路通訊人才培育先導型計畫 Probability, Random Processes and Noise 1 Several random variables The joint distribution function is the probability that the outcomes of an experiment will result in a sample point lying inside the quadrant of the joint sample space. Suppose is continuous everywhere, and the partial derivative exist and is continuous everywhere. is called the joint probability density function of the random variables X and Y. 5.2

2. 教育部網路通訊人才培育先導型計畫 Probability, Random Processes and Noise 2 Marginal pdf and conditional pdf The pdfs and are called marginal densities. The conditional probability density function of Y given that X=x is defined by It satisfies all the requirements of an ordinary pdf, as shown by and 5.2

3. 教育部網路通訊人才培育先導型計畫 Probability, Random Processes and Noise 3 Example 5-3 Marginal and conditional pdfs (1/3) Suppose the joint pdf for two random variable is (a) Find the marginal density for Y, and (b) the conditional probability density. 5.2

4. 教育部網路通訊人才培育先導型計畫 Probability, Random Processes and Noise 4 Example 5-3 Marginal and conditional pdfs (2/3) (a) The marginal density for Y is 5.2 【 Sol. 】

5. 教育部網路通訊人才培育先導型計畫 Probability, Random Processes and Noise 5 Example 5-3 Marginal and conditional pdfs (3/3) (b) the conditional probability density is 5.2