Concept explainers
a.
Estimate the value of c.
a.
Answer to Problem 18E
The value of c is 1.2.
Explanation of Solution
The probability density
The value of k is calculated below:
Thus, the value of c is 1.2.
b.
Find the value of
b.
Answer to Problem 18E
The value of
Explanation of Solution
The value of
The value of
The value of
The value of
Thus, the value of F(y) is
c.
Draw a graph of f(y)
Draw a graph of F(y)
c.
Answer to Problem 18E
The graph of f (y) and F (y) is given below:
In the above graph the solid line indicates the f (y) and the dotted line indicates the F(y).
Explanation of Solution
Calculate the values of the density function as shown in table below:
y | |
–1 | 0.2 |
–0.75 | 0.2 |
–0.5 | 0.2 |
–0.25 | 0.2 |
0 | 0.2 |
0.25 | 0.5 |
0.5 | 0.8 |
0.75 | 1.1 |
1 | 1.4 |
Calculate the values of the distribution function as shown in table below:
y | |
–1 | 0 |
–0.75 | 0.05 |
–0.5 | 0.1 |
–0.25 | 0.15 |
0 | 0.2 |
0.25 | 0.2875 |
0.5 | 0.45 |
0.75 | 0.6875 |
1 | 1 |
To sketch the graph, provide the values of y in vertical axis and the values of f (y) and F (y) in horizontal axis, and join the points to obtain the respective graphs of f (y) and F (y).
d.
Find the value
Find the value
Find the value
d.
Answer to Problem 18E
The value
The value
The value
Explanation of Solution
From Part b, it can be observed that
The value
The value
The value
Thus, the value
Thus, the value
Thus, the value
e.
Find the value of
e.
Answer to Problem 18E
The value of
Explanation of Solution
The value of
Thus, the value of
f.
Find the value of
f.
Answer to Problem 18E
The value of
Explanation of Solution
The value of
Thus, the value of
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Chapter 4 Solutions
Mathematical Statistics with Applications
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