Consider the following joint distribution.
X
p(x,y)
2
4
Y
1
0.11
0.36
6
0.33
0.2
Based on this distribution, fill in the blanks below.
X
p(x,y)
2
4
Y
1
0.11
0.36
6
0.33
0.2
E(X)=
Sd(Y)= .
Corr(X,Y)=
X
19
20
21
22
23
P(x)
0.21
0.25
0.31
0.13
0.1
Find the mean, variance, and standard deviation of the
distribution rounded to 4 decimal places.
Mean =
Variance =
Standard Deviation =
Approximately how many arrangements should the florist expect to
deliver each week, rounded to the nearest whole number?
Let X and Y have joint discrete distribution p(x, y) = 3 20 (.5
x ) (.7 y ), x = 0, 1, 2, . . . , and y = 0, 1, 2, . . .. Find the
marginal probability function P(X = x). [hint: for a geometric
series X∞ n=0 arn with −1 < r < 1, r 6= 0, then X∞ n=0 arn =
a 1 − r ]
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...
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)
Let X and Y have the following joint distribution:
X/Y
0
1
2
0
5/50
8/50
1/50
2
10/50
1/50
5/50
4
10/50
10/50
0
Further, suppose σx = √(1664/625), σy = √(3111/2500)
a) Find Cov(X,Y)
b) Find p(X,Y)
c) Find Cov(1-X, 10+Y)
d) p(1-X, 10+Y), Hint: use c and find Var[1-X], Var[10+Y]
Consider the following data:
x 4 5 6 7 8
P(X=x) 0.1 0.3 0.1 0.2 0.3
Step 1 of 5: Find the expected value E(X). Round your answer to
one decimal place.
Step 2 of 5:
Find the variance. Round your answer to one decimal place.
Step 3 of 5:
Find the standard deviation. Round your answer to one decimal
place.
Step 4 of 5:
Find the value of P(X>6)P(X>6). Round your answer to one
decimal place.
Step 5 of...
let p ( x , y )be a joint pmf of Xand Y.
p ( x , y )
y = 0
y = 1
y = 2
x = 0
.12
.10
.08
x = 1
.13
.17
.10
x = 2
.15
.15
0
(a) Find the marginal pmf's of Xand Y.
(b) Determine whether Xand Yare independent.
c) Find Correlation (X,Y)
Consider the following data:
x
-4
-3
-2
-1
0
P(X=x)
0.2
0.1
0.2
0.1
0.4
Step 2 of 5 : Find the variance. Round your answer to one
decimal place.
Step 3 of 5 : Find the standard deviation. Round your answer to
one decimal place.
1. Consider the probability distribution shown below.
x
0
1
2
P(x)
0.25
0.60
0.15
Compute the expected value of the distribution. (Enter a
number.)
Compute the standard deviation of the distribution. (Enter a
number. Round your answer to four decimal places.)
2. What is the income distribution of super shoppers? A
supermarket super shopper is defined as a shopper for whom
at least 70% of the items purchased were on sale or purchased with
a coupon. In the following...