The random variables X and Y have the joint PMF p_{X,Y}(x,y) = { cxy, x = 1, 2, 3; y = 1, 2, 0 otherwise. Find (a) the constant c, (b) the expected values E(X) and E(Y), (c) the second moments E(X^2) and E(Y^2).
Added by Kathleen C.
Close
Step 1
We know that the sum of all probabilities in a joint PMF must equal 1. So, we have: C * (sum of all x*y for x = 1, 2, 3 and y = 1, 2) = 1 C * (1*1 + 1*2 + 2*1 + 2*2 + 3*1 + 3*2) = 1 C * (22) = 1 C = 1/22 Now that we have the constant C, we can find the Show more…
Show all steps
Your feedback will help us improve your experience
Madhur L and 51 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 PMF of random variables X and Y is given by the following table. YX 1 2 3 1 3c c 6c 2 2c 0 4c 3 c c 2c (a) Find constant c, pY(1) and pY(3) . (b) Let Z=YX2. Find E[Z|Y=3].
Jon S.
Suppose X and Y are 2 discrete random variables. Given the PMF of Y conditional on X, and the marginal PMF of X: (a) Find and tabulate the joint PMF of X and Y (b) Find E(X^2), E(Y) (c) Find E(X^2Y), Cov(X^2,Y) (d) Find and tabulate the conditional probability P_X|Y = 1(x), for x = 1,2,3 (e) Find E(X|Y = 1), Var(X|Y = 1)
Sri K.
Let X and Y have the joint pmf f(x, y) = e^(-2/[x!(y - x)!]), y = 0, 1, 2, ...; x = 0, 1, ..., y, zero elsewhere. (a) Find the moment-generating function M(t1, t2) of this joint distribution. (b) Compute the means, the variances, and the correlation coefficient of X and Y. (c) Determine the conditional mean E(X|Y = y). Hint: Note that Py x=0[exp(t1x)]y!/[x!(y - x)!] = [1 + exp(t1)]^y.
Shaiju T.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD