E) Ailt anu1 uependent or i ndependent? Why or why ow? Assu not? 4.1-3. Let the...
Let the joint pmf of X and Y be defined by x+y 32 x 1,2, y,2,3,4 (a) Find fx(x), the marginal pmf of X. b) Find fyv), the marginal pmf of Y (c) Find P(XsY. (d) Find P(Y 2x). (e) Find P(X+ Y 3) (f) Find PX s3-Y) (g) Are Xand Y independent or dependent?Why or why not? (h) Find the means and the variances of X and Y
Q: Asking for assistance in understanding and solving this example on Probability and Statistical with the steps of the solution to better understand, thanks. **Please give the step by steps with details to completely see how the solution came about. 1) Let the joint pmf of X and Y be defined by: f(x,y) = (x+y)/(33), x=1,2, y=1,2,3. (a) Find fx(x), the marginal pmf of X. (b) Find fy(y), the marginal pmf of Y. (c) Find P(X >...
I don't understand what this is asking me to do. 4.1-7.)A particle starts at (0, 0) and moves in one-unit dependent steps with equal probabilities of 1/4 in each of the four directions: north, south, east, and west. Let S equal the east-west position and T the north-south position after n steps. (a) Define the joint pmf of S and T with n = 3. On a two-dimensional graph, give the probabilities of the joint pmf and the marginal pmfs...
3. Let f(x,y) = xy-1 be the joint pmf/ pdf of two random variables X (discrete) and Y (continuous), for x = 1, 2, 3, 4 and 0 <y < 2. (a) Determine the marginal pmf of X. (b) Determine the marginal pdf of Y. (c) Compute P(X<2 and Y < 1). (d) Explain why X and Y are dependent without computing Cou(X,Y).
4.2 The Correlation Coefficient 1. Let the random variables X and Y have the joint PMF of the form x + y , x= 1,2, y = 1,2,3. p(x,y) = 21 They satisfy 11 12 Mx = 16 of = 12 of = 212 2 My = 27 Find the covariance Cov(X,Y) and the correlation coefficient p. Are X and Y independent or dependent?
4. Let X denote the number eggs hatched out of Y eggs laid by a particular parasite. The joint pmf of (X, Y) is given by A(1-0) e ,for x 0, 1, 2,.., y , and y = 0,1,2, .,00 Px,y (x, y)= 1 -6 = 0, otherwise where A> 0 and 0< 0<1 are unknown constants. (a) Find the marginal pmfs of X and Y. Are X and Y independent? (b) Find the conditional pmf of X|Y = y...
probability, show all work 7. Let 3 cards be taken at random and without replacement from an ordinary deck of cards. Let X be the number of spades and Y be the number of hearts. Find (1) pmf of X (2) Joint pmf of X and Y. (3) P(X 2,Y 1). (10 Points)
I just need the second problem done. Problem #2 refers to the problem #1. Problem # 1. Let discrete random variables X and Y have joint PMF cy 2,0,2 y=1,0, 1 otherwise = Px.y (x, y) 0 Find: a) Constant c X], P[Y <X], P[X < 1 b) P[Y 2. Let X and Y be the same as in Problem # 1. Find: Problem a) Marginal PMFs Px() and Py(y) b) Expected values E[X] and E[Y] c) Standard deviations ox...
Problem 3 Let X and Y have joint pdf: fxy(x, y) = k(x + y) for 0 sxs1,0 s y s 1. (a) Find k. (b) Find the joint cdf of (X, Y). (c) Find the marginal pdf of X and of Y. (d) Find P[X < Y), P[Y < X²), P[X + Y > 0.5). (a) Find E[(X + Y)?]. (b) Find the variance of X + Y. (c) Under what condition is the variance of the sum equal...
ciule jolh! PMF and the marginal PMFs? 6.14 Let X and Y be discrete random variables. Show that the function p: R2 R defined by p(r, y) px(x)pr(y) is a joint PMF by verifying that it satisfies properties (a)-(c) of Proposition 6.1 on page 262. Hint: A subset of a countable set is countable CHAPTER SIX Joindy Discrete Random Variables 6.2 Joint and marginal PMFs of the discrete random variables x numher of bedrooms and momber of bwthrooms of a...