Question
In: Statistics and Probability
You are given the joint probability distribution: (x+2y)/30 for x = 1, 2 and y =...
You are given the joint probability distribution: (x+2y)/30 for x = 1, 2 and y = 2, 4.
Calculate Var(5X – 4Y).
Solutions
orchestra answered 2 years agoRelated Solutions
If the joint probability distribution of X and Y f(x, y) = (x + y)/2
If the joint probability distribution of X and Y f(x, y) = (x + y)/2, x=0,1,2,3; y=0,1,2, Compute the following a. P(X≤2,Y =1) b. P(X>2,Y ≤1) c. P(X>Y) d. P(X+Y=4)
Suppose the joint probability distribution of X and Y is given by the following table. Y=>3...
Suppose the joint probability distribution of X and Y is given
by the following table.
Y=>3 6 9 X
1 0.2 0.2 0
2 0.2 0 0.2
3 0 0.1 0.1
The table entries represent the probabilities. Hence the
outcome [X=1,Y=6] has probability
0.2.
a) Compute E(X), E(X2), E(Y), and E(XY). (For all answers show
your work.) b) Compute E[Y | X = 1], E[Y | X = 2], and E[Y | X =
3].
c) In this case, E[Y...
Suppose the joint probability distribution of two binary random variables X and Y are given as...
Suppose the joint probability distribution of two binary random
variables X and Y are given as follows.
x/y
1
2
0
3/10
0
1
4/10
3/10
X goes along side as 0 and 1, Y goes along top as 1 and 2
e) Find joint entropy H(X, Y ).
f) Suppose X and Y are independent. Show that H(X|Y ) =
H(X).
g) Suppose X and Y are independent. Show that H(X, Y ) = H(X) +
H(Y ).
h)...
5. Suppose that X and Y have the following joint probability distribution: f(x,y) x 2 4...
5. Suppose that X and Y have the following joint probability
distribution:
f(x,y)
x
2
4
y
1
0.10
0.15
2
0.20
0.30
3
0.10
0.15
Find the marginal distribution of X and Y.
Find the expected value of g(x,y) = xy2 or find E(xy2).
Find (x and (y.
Find Cov(x,y)
Find the correlations ρ(x,y)
3.
The length of life X, in days, of a heavily used electric motor
has probability density function
Find the probability that the motor has...
. The joint probability density function of X and Y is given by ?(?, ?) =...
. The joint probability density function of X and Y is given
by
?(?, ?) = { ??^2? ?? 0 ≤ ? ≤ 2, 0 ≤ ?, ??? ? + ? ≤ 1
0 ??ℎ??????
(a) Determine the value of c.
(b) Find the marginal probability density function of X and
Y.
(c) Compute ???(?, ?).
(d) Compute ???(?^2 + ?).
(e) Determine if X and Y are independent
The joint probability distribution of variables X and Y is shown in the table below. ...............................................................................X..........................................................................
The joint probability distribution of variables X and
Y is shown in the table below.
...............................................................................X.......................................................................
Y
1
2
3
1
0.30
0.18
0.12
2
0.15
0.09
0.06
3
0.05
0.03
0.02
Calculate E(XY)
Determine the marginal probability distributions of X
and Y.
Calculate E(X) and E(Y)
Calculate V(X) and V(Y)
Are X and Y independent? Explain.
Find P(Y = 2| X = 1)
Calculate COV(X,Y). Did you expect
this answer? Why?
Find the probability distribution...
Suppose that the joint probability density function of ˜ (X, Y) is given by:´ f X,Y...
Suppose that the joint probability density function of ˜ (X, Y) is given by:´
f X,Y (x,y) = 4x/y3 I(0.1)(x), I (1, ∞)(y).
Calculate
a) P(1/2 < X < 3/4, 0 < Y ≤ 1/3).
b) P(Y > 5).
c) P(Y > X).
Determine the correlation for the following joint probability distribution: x 2 4 2 4 y 3...
Determine the correlation for the following joint probability
distribution:
x
2
4
2
4
y
3
4
5
6
fx,y(x,y)
1/8
1/4
1/2
1/8
a.
Correlation = 0.6387
b.
Correlation = 0.0377
c.
Correlation = 0.3737
d.
Correlation = 0.8023
The joint probability distribution of the number X of cars and the number Y of buses...
The joint probability distribution of the number X of
cars and the number Y of buses per signal cycle at a
proposed left-turn lane is displayed in the accompanying joint
probability table.
y
p(x,
y)
0
1
2
x
0
0.015
0.025
0.010
1
0.030
0.050
0.020
2
0.075
0.125
0.050
3
0.090
0.150
0.060
4
0.060
0.100
0.040
5
0.030
0.050
0.020
(a) What is the probability that there is exactly one car and
exactly one bus during...
The joint probability distribution of the number X of cars and the number Y of buses...
The joint probability distribution of the number X of
cars and the number Y of buses per signal cycle at a
proposed left-turn lane is displayed in the accompanying joint
probability table.
y
p(x,
y)
0
1
2
x
0
0.015
0.010
0.025
1
0.030
0.020
0.050
2
0.075
0.050
0.125
3
0.090
0.060
0.150
4
0.060
0.040
0.100
5
0.030
0.020
0.050
(a) What is the probability that there is exactly one car and
exactly one bus during...
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