| << Chapter < Page | Chapter >> Page > |
for , (see Exercise 12 from "Problems on Random Vectors and Joint Distributions").
From the solution for Exercise 12 from "Problems on Random Vectors and Joint Distributions" we have
so the pair is independent.
tuappr
Enter matrix [a b]of X-range endpoints [0 1]
Enter matrix [c d]of Y-range endpoints [0 1]
Enter number of X approximation points 100Enter number of Y approximation points 100
Enter expression for joint density 4*t.*(1-u)Use array operations on X, Y, PX, PY, t, u, and Pitest
Enter matrix of joint probabilities PThe pair {X,Y} is independent for , (see Exercise 13 from "Problems on Random Vectors and Joint Distributions").
From the solution of Exercise 13 from "Problems on Random Vectors and Joint Distributions" we have
so which implies the pair is not independent.
tuappr
Enter matrix [a b]of X-range endpoints [0 2]
Enter matrix [c d]of Y-range endpoints [0 2]
Enter number of X approximation points 100Enter number of Y approximation points 100
Enter expression for joint density (1/8)*(t+u)Use array operations on X, Y, PX, PY, t, u, and P
itestEnter matrix of joint probabilities P
The pair {X,Y} is NOT independentTo see where the product rule fails, call for D for (see Exercise 14 from "Problems on Random Vectors and Joint Distributions").
From the solution for Exercise 14 from "Problems on Random Vectors and Joint Distribution" we have
so that and the pair is independent.
tuappr
Enter matrix [a b]of X-range endpoints [0 5]
Enter matrix [c d]of Y-range endpoints [0 1]
Enter number of X approximation points 500Enter number of Y approximation points 100
Enter expression for joint density 4*u.*exp(-2*t)Use array operations on X, Y, PX, PY, t, u, and P
itestEnter matrix of joint probabilities P
The pair {X,Y} is independent % Product rule holds to within 10^{-9} on the parallelogram with vertices
(see Exercise 16 from "Problems on Random Vectors and Joint Distributions").
Not independent by the rectangle test.
tuappr
Enter matrix [a b]of X-range endpoints [-1 1]
Enter matrix [c d]of Y-range endpoints [0 1]
Enter number of X approximation points 200Enter number of Y approximation points 100
Enter expression for joint density 12*t.^2.*u.*(u<=min(t+1,1)).* ...
(u>=max(0,t))
Use array operations on X, Y, PX, PY, t, u, and Pitest
Enter matrix of joint probabilities PThe pair {X,Y} is NOT independent
To see where the product rule fails, call for D for , (see Exercise 17 from "Problems on Random Vectors and Joint Distributions").
By the rectangle test, the pair is not independent.
tuappr
Enter matrix [a b]of X-range endpoints [0 2]
Enter matrix [c d]of Y-range endpoints [0 1]
Enter number of X approximation points 200Enter number of Y approximation points 100
Enter expression for joint density (24/11)*t.*u.*(u<=min(1,2-t))
Use array operations on X, Y, PX, PY, t, u, and Pitest
Enter matrix of joint probabilities PThe pair {X,Y} is NOT independent
To see where the product rule fails, call for D 
Notification Switch
Would you like to follow the 'Applied probability' conversation and receive update notifications?
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|