1. The covariance between X and Y is 6.5. Sx = 7.2 and Sy = 3.6
Hence, the value of rxy is: _________________ (1 point)
2. Given that r = + 0.32, Sx = 5.2, and Sy = 6.4, the covariance
equals: _________________ (1 point)
3. For a particular set of data, Sx = 9.2 and Sy = 8.5. What is
the largest possible value of the covariance?
_________________ (2 points)
4. For a particular set of data, Sx =...
Let the joint pmf of X and Y be defined by f (x, y) = c(x + y),
x =0, 1, 2, y = 0, 1, with y ≤ x.
1. Are X and Y independent or dependent? Why or why not?
2. Find g(x | y) and draw a figure depicting the conditional
pmfs for y =0 and 1.
3. Find h(y | x) and draw a figure depicting the conditional
pmfs for x = 0, 1 and2.
4....
Let the joint pmf of X and Y be defined by f (x, y) = c(x + y),
x =0, 1, 2, y = 0, 1, with y ≤ x.
1. Find g(x | y) and draw a figure depicting the conditional
pmfs for y =0 and 1.
2. Find h(y | x) and draw a figure depicting the conditional
pmfs for x = 0, 1 and2.
3. Find P(0 < X <2 |Y = 0), P(X ≤ 2 |Y...
f(x) = -3x2+16x-5
e) Find (in y=mx+b form) the equation of the line that contains
the vertex and the largest of the x-axis intercepts. If there are
decimals round to the tenths place.
f) Find the length of the line segment that is between the
vertex and the largest of the x-axis intercepts.
The joint pmf of (X,Y) is depicted below.
f(x,y)
y=0
y-=1
y=2
y=3
x=0
0.02
0.05
0.06
0.12
x=1
0.03
0.12
0.15
0.13
x=2
0.02
0.10
0.15
0.05
a.) What is the marginal pmf of X.
b.) Calculate E(X).
c.) What is the conditional pmf (probability mass function) of X
given that Y = 1.
d.) Calculate E(X | Y = 1).
e.) Calculate Var(X | Y = 1).
f.) What is the cov(X,Y)? Note cov means
covariance
2. The joint pmf of ? and ? is given by
??,? (?, ?) = (x+y)/27 ??? ? = 0, 1,2; ? = 1, 2,
3,
and ??,? (?, ?) = 0 otherwise.
a. Find ?(?|? = ?) for all ? = 0,1, 2.
b. Find ?(3 + 0.2?|? = 2).
Let the random variable X and Y have the joint pmf f(x, y) = , c
xy 2 where x = 1, 2, 3; y = 1, 2, x + y ≤ 4 , that is, (x, y) are
{(1, 1),(1, 2),(2, 1),(2, 2),(3, 1)} .
(a) Find c > 0 .
(b) Find μ . X
(c) Find μ . Y
(d) Find σ . 2 X
(e) Find σ . 2 Y
(f) Find Cov (X, Y )...
3. Given is the function f : Df → R with F(x1, x2, x3) = x 2 1 +
2x 2 2 + x 3 3 + x1 x3 − x2 + x2 √ x3 . (a) Determine the gradient
of function F at the point x 0 = (x 0 1 , x0 2 , x0 3 ) = (8, 2,
4). (b) Determine the directional derivative of function F at the
point x 0 in the direction given...
Let the random variable and have the joint pmf X Y f(x,y) =
{x(y)^2}/c
where x = 1, 2, 3 ; y = 1, 2, x+y<= 4, that is (x,y) are {(1,1),
(1,2), (2,1), (2,2), 3,1)}
(a) Find . c > 0
(b) Find . μX
(c) Find . μY
(d) Find . σ2 X
(e) Find . σ2 Y
(f) Find Cov . (X,Y )
(g) Find p , Corr . (x,y)
(h) Are and X and Y independent