Question

The independent random variables X and Y are defined by the following probability distribution tables: X 1 3 6 f(x) 0.6 0.3 0.1 Y 2 3 5 7 f(y) 0.1 0.2 0.3 0.4Determine the standard deviation of 3Y + 5

Answer #1

Let X and Y be independent discrete random variables with
pmf’s:
x
1
2
3
y
2
4
6
p(x)
0.2
0.2
0.6
p(y)
0.3
0.1
0.6
What is the probability that X + Y = 7

Three tables listed below show random variables and their
probabilities. However, only one of these is actually a probability
distribution. A B C x P(x) x P(x) x P(x) 25 0.3 25 0.3 25 0.3 50
0.1 50 0.1 50 0.1 75 0.2 75 0.2 75 0.2 100 0.4 100 0.6 100 0.8 a.
Which of the above tables is a probability distribution? b. Using
the correct probability distribution, find the probability that x
is: (Round the final answers to...

Three tables listed below show random variables and their
probabilities. However, only one of these is actually a probability
distribution.
A
B
C
X
P(X)
X
P(X)
X
P(X)
5
0.1
5
0.1
5
0.1
10
0.3
10
0.3
10
0.3
15
0.4
15
0.4
15
0.4
20
0.2
20
0.4
20
0.6
a. Which is it?
(Click to select) B C A
b. Using the correct probability distribution,
find the probability that x is: (Round the final
answers to 1 decimal place.)...

A random variable x has the following probability distribution.
Determine the standard deviation of x.
x
f(x)
0
0.05
1
0.1
2
0.3
3
0.2
4
0.35
A random variable x has the following probability distribution.
Determine the expected value of x.
x
f(x)
0
0.11
1
0.04
2
0.3
3
0.2
4
0.35
QUESTION 2
A random variable x has the following probability distribution.
Determine the variance of x.
x
f(x)
0
0.02
1
0.13
2
0.3
3
0.2...

The probability distribution of a couple of random variables (X,
Y) is given by :
X/Y
0
1
2
-1
a
2a
a
0
0
a
a
1
3a
0
a
1) Find "a"
2) Find the marginal distribution of X and Y
3) Are variables X and Y independent?
4) Calculate V(2X+3Y) and Cov(2X,5Y)

Three tables listed below show random variables and their
probabilities. However, only one of these is actually a probability
distribution.
A
B
C
x
P(x)
x
P(x)
x
P(x)
25
0.1
25
0.1
25
0.1
50
0.3
50
0.3
50
0.3
75
0.4
75
0.4
75
0.4
100
0.2
100
0.4
100
0.6
a. Which of the above tables is a probability
distribution?
(Click to select)BAC
b. Using the correct probability distribution,
find the probability that x is: (Round the...

Three tables listed below show random variables and their
probabilities. However, only one of these is actually a probability
distribution.
A
B
C
X
P(X)
X
P(X)
X
P(X)
5
0.3
5
0.1
5
0.5
10
0.3
10
0.2
10
0.3
15
0.2
15
0.3
15
−0.2
20
0.4
20
0.4
20
0.4
b. Using the correct probability distribution,
find the probability that x is: (Round the final
answers to 1 decimal place.)
1.
Exactly 15 =
2.
No...

Consider joint Probability distribution of two random variables
X and Y given as following
f(x,y) X
2 4 6
Y 1 0.1 0.15
0.06
3 0.17 0.1
0.18
5 0.04 0.07
0.13
(a) Find expected value of g(X,Y) = XY2
(b) Find Covariance of Cov(x,y)

Three tables listed below show random variables and their
probabilities. However, only one of these is actually a probability
distribution.
A
B
C
x
P(x)
x
P(x)
x
P(x)
25
0.1
25
0.1
25
0.1
50
0.1
50
0.1
50
0.1
75
0.6
75
0.6
75
0.6
100
0.2
100
0.4
100
0.6
a. Which of the above tables is a probability
distribution?
(Click to select) A C B
b. Using the correct probability distribution,
find the probability that x is: (Round the...

The joint probability distribution of two random variables X and
Y is given in the following table
X Y →
↓
0
1
2
3
f(x)
2
1/12
1/12
1/12
1/12
3
1/12
1/6
1/12
0
4
1/12
1/12
0
1/6
f(y)
a) Find the marginal density of X and the marginal density of Y.
(add them to the above table)
b) Are X and Y independent?
c) Compute the P{Y>1| X>2}
d) Compute the expected value of X.
e)...

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