Contents
How do you calculate conditional pdf?
If X and Y are independent, the conditional pdf of Y given X = x is f(y|x) = f(x, y) fX(x) = fX(x)fY (y) fX(x) = fY (y) regardless of the value of x.
How do you find conditional proportions?
We obtain the conditional proportions per row by dividing the value in each cell by the row total. We can index a row from our data using [,] . For example, data[1,] would index the first row (enter it into your console and have a look!). We can find the sum (or total) value in R using the function sum() .
Which is the correct conditional distribution for Y?
X;Y continuous: the conditional pdf of X given Y = y is de ned to be f XjY (xjy) = f(x;y) f Y (y); f Y (y) > 0: Given Y = y, f(x;y) is NOT a pdf wrt x, since R f(x;y)dx = f Y (y) 6= 1 : So we need f Y (y) in the denominator to make it a legit pdf. Check theWolfram Demo. 2
How to calculate the probability of a joint probability distribution?
There are 6 possible pairs (X;Y). We show the probability for each pair in the following table: x=length 129 130 131 y=width 15 0.12 0.42 0.06 16 0.08 0.28 0.04 The sum of all the probabilities is 1.0. The combination with the highest probabil- ity is (130;15). The combination with the lowest probability is (131;16).
Which is an example of a discrete joint PMF?
Example: Plastic covers for CDs (Discrete joint pmf) Measurements for the length and width of a rectangular plastic covers for CDs are rounded to the nearest mm(so they are discrete). Let Xdenote the length and Y denote the width. The possible values of Xare 129, 130, and 131 mm.
Which is the independence of a joint distribution?
Joint Distributions (for two or more r:v:’s) Marginal Distributions (computed from a joint distribution) Conditional Distributions (e.g. P(Y = yjX= x)) Independence for r:v:’s Xand Y. This is a good time to refresh your memory on double-integration.