The joint density function of the random variables X and Y is f(x, y) = 6x 0 < x < 1, 0 < y < 1 − x a. Show that X and Y are not independent. b. Find f(x|y) and use it to find P(X > 0.3|Y = 0.5)
Added by Megan N.
Step 1
To show that X and Y are not independent, we need to show that the joint density function f(x, y) is not equal to the product of the marginal density functions f(x) and f(y). The marginal density function of X, f(x), is obtained by integrating f(x, y) over all Show more…
Show all steps
Close
Your feedback will help us improve your experience
Chai Santi and 73 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The joint density function of the random variables X and Y is f(x, y) = 6x, 0 < x < 1, 0 < y < 1 − x, 0, elsewhere. (a) Show that X and Y are not independent. (b) Find P(X >0.3 | Y = 0.5).
Rashmi S.
The joint density function of the random variables X and Y is given to the right. (a) Show that X and Y are not independent. (b) Find P(X > 0.3 | Y = 0.4). f(x,y) = { 6x, 0 < x < 1, 0 < y < 1 - x 0, elsewhere (a) Select the correct choice below and fill in the answer box to complete your choice. A. Since f(x|y) = f(x,y) / h(y) = , for 0 < x < 1 - y, is constant, X and Y are not independent. B. Since f(x|y) = f(x,y) / h(y) = , for 0 < x < 1 - y, is a function of only the variable x, X and Y are not independent. C. Since f(x|y) = f(x,y) / h(y) = 3/4, for 0 < x < 1 - y, involves the variable y, X and Y are not independent. D. Since f(x|y) = f(x,y) / h(y) = , for 0 < y < 1 - x, involves the variable x, X and Y are not independent.
Sri K.
The joint density function for a pair of random variables $ X $ and $ Y $ is $ f(x, y) = \left\{ \begin{array}{ll} Cx (1 + y) & \mbox{if $ 0 \le x \le 1, 0 \le y \le 2 $}\\ 0 & \mbox{otherwise} \end{array} \right.$ (a) Find the value of the constant $ C $. (b) Find $ P(X \le 1, Y \le 1) $. (c) Find $ P(X + Y \le 1) $.
Multiple Integrals
Applications of Double Integrals
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD