Let X be a Poisson (mean = 5) and Let Y be a Poisson (mean = 4). Let Z = X + Y. Find P( X = 3 | Z = 6). Assume X and Y are independent. Show answers for P(A), P(B), P(AB), and and hence P(A|B). Here A = [X = 3], B = [Z = 6]
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
2,Let X be a Poisson (mean-5) and Let Ybe a Poisson (mean-4). Let Z-X+Y.Find P(X-312-6) Assume X and Y are independent. 1 like to see answers for P(A), (B), P(AB), and and hence P(A B). Here A You can work out the probabilities (P(A).P(B),P(AB), and P(AIB) using your calculator, or Minitab or Mathematica. I dont need to see your commands.I just like to see the answers for the probabilities of ABABAIB You do item 1 lf your FSU id ends...
Let X, Y Geometric(p) be independent, and let Z a. Find the range of 2. b. Find the PMF of Z c. Find EZ.
Let X, Y Geometric(p) be independent, and let Z a. Find the range of 2. b. Find the PMF of Z c. Find EZ.
0, otherwise Let f(x,y)= 2. a. Sketch the region of integration b. Find k c. Find the marginal density of X d. Find the marginal density of Y e. Find P(Y > 0/X = 0.50)
0, otherwise Let f(x,y)= 2. a. Sketch the region of integration b. Find k c. Find the marginal density of X d. Find the marginal density of Y e. Find P(Y > 0/X = 0.50)
2. Let the joint probability density function of (X, Y) be given by {ay otherwise. 1 and 0 < y < 2, f(z,y) (a) [6 pts] Determine if X and Y are independent. (b) [6 pts] Find P{X+Y <1) B( (c) [6 pts) Find
2. Let the joint probability density function of (X, Y) be given by {ay otherwise. 1 and 0
Let the joint pdf of X and Y be defined by f(x,y)=\frac{x+y}{32} x=1,2, y=1,2,3,4 a) find fx(x), the marginal p.d.f of X b) find fy(y). the marginal p.d.f of p(x>y),p(y=2x) f) find P(x<= 3-Y) g) Are X and Y independent or dependent? Why or why not?
2. Let the random variables X and Y have the joint PDF given
below:
(a) Find P(X + Y ≤ 2).
(b) Find the marginal PDFs of X and Y.
(c) Find the conditional PDF of Y |X = x.
(d) Find P(Y < 3|X = 1).
Let the random variables X and Y have the joint PDF given below: 2e -0 < y < 00 xY(,) otherwise 0 (a) Find P(XY < 2) (b) Find the marginal PDFs of...
6. Let f(x,y) = 1 if 0 < y < 2x, 0<x<1, and 0 otherwise. Find the following: a) f(y|x) b) E(Y|X = x) c) The correlation coefficient, p, between X and Y
5. (40 points) Let f(x,y) = (x + y),0 < 2,2 <y < 1 be the joint pdf of X and Y. (1) Find the marginal probability density functions fx(x) and fy(y). (2) Find the means hx and my. (3) Find P(X>01Y > 0.5). (4) Find the correlation coefficient p.