Give the marginal pmf of X in the margin. Give the marginal pmf of Y in the marg

Question

Give the marginal pmf of X in the margin. Give the marginal pmf of Y in the margin. Are X and Y dependent or independent? Why or Why not? Let the joint pmf of X and Y be defined by f(x, y) = x + y/32, x = 1,2 y = 1, 2, 3,4. Find f_x(x), the marginal pmf of X. Find f_y(y), the marginal pmf of Y. Find P(X > Y). Find P(Y = 2X). Find P(X + Y = 3). Find P(x lessthanorequalto 3 - Y). Are X and Y independent or dependent? Why or why not? Find the means and the variances of X and Y. Select an (even) integer randomly from the set {0, 2, 4, 6, 8}. Then select an integer randomly from the set {0 1 2 3 4}. Let X equal the integer that is selected from the first set and let Y equal the sum of the two integers.

Explanation / Answer

A) fx(x)=f(x,1)+f(x,2)+f(x,3)+f(x,4)

=(x+1)/32 + (x+2)/32

=(2x+3)/32

B) fy(y)=f(1,y)+f(2,y) +f(3,y)+f(4,y)

=(1+y)/32 +(2+y)/32 +(3+y)/32+(4+y)/32

=(4y+10)/32

=(2y+5)/16
C)P(X>Y)=f(2,1)

=(2+1)/32

=3/32

=0.09375

D)P(y=2x)=f(1,2)+f(2,4)

=3/32+6/32

=9/32

=0.28125

E)P(X+Y=3)=f(1,2)+f(2,1)

=3/32+3/32

=3/16

=0.1875

F)

P(x<=3-y)=P(x+y<=3)

=f(1,1)+f(1,2)+f(2,1)

=2/32+3/32+3/32

=1/4

=0.25

g) here x and y are depend variables beacuse if you change one value automatically another variable will change

h) the mean is the sum of the valuesthen

6/32

the variance of x and y is

6/32-0.88

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.