Stat ps 5

Blackboard Problem Set #6a

1.
Consider the joint probability distribution of X and Y:

x = 2 x = 4 y = 1
0.3
0.2 y = 2
0.1
0.4

What is E(X|y = 1) (rounded to four decimal places)?

2.
Consider the joint probability distribution of X and Y:

x = 2 x = 4 y = 1
0.3
0.2 y = 2
0.1
0.4

What is E(Y|x = 4) (rounded to four decimal places)?

3.
Undergraduates are asked to write a 300-word essay. The number of non-word (N) errors is a random variable that has the following distribution:

n
0
1
2
P(n)
0.1
0.4
0.5

The number of word (W) errors is a random variable that has the following distribution:

w
0
1
2
P(w)
0.2
0.6
0.2

Suppose the correlation between non-word errors and word errors is 0.5. What is the mean of the total number of errors (μN+W) (rounded to four decimal places)?

4.
Undergraduates are asked to write a 300-word essay. The number of non-word (N) errors is a random variable that has the following distribution:

n
0
1
2
P(n)
0.1
0.4
0.5

The number of word (W) errors is a random variable that has the following distribution:

w
0
1
2
P(w)
0.2
0.6
0.2

Suppose the correlation between non-word errors and word errors is 0.5. What is the standard deviation of the total number of errors (σN+W) (rounded to four decimal places)?

5.
Consider the joint probability distribution of X and Y:

x = 0 x = 1 y = 0
0.1
0.4 y = 1
0.1
0.4

In this example, X and Y are _____. In this example, X and Y are _____.
A)
independent, correlated
B)
independent, uncorrelated
C)
not independent, correlated
D)
not independent, uncorrelated

6.
Consider the joint probability distribution of X and Y:

x = 0 x = 1 y = 0
0.2
0.2 y = 1
0.1
0.5

In this example, X and Y are _____. In this example, X and Y are _____.
A)
independent,