Solution Found!
For each of the following, determine the constant c so that f(x) satisfies the
Chapter 2, Problem 2.1-3(choose chapter or problem)
For each of the following, determine the constant c so that f(x) satisfies the conditions of being a pmf for a random variable X, and then depict each pmf as a line graph:
(a) \(f(x)=x / c, \quad x=1,2,3,4\)
(b) \(f(x)=c x, \quad x=1,2,3, \ldots, 10\)
(c) \(f(x)=c(1 / 4)^{x}, \quad x=1,2,3, \ldots\)
(d) \(f(x)=c(x+1)^{2}, \quad x=0,1,2,3\)
(e) \(f(x)=x / c, \quad x=1,2,3, \ldots, n\).
(f) \(f(x)=\frac{c}{(x+1)(x+2)}, \quad x=0,1,2,3, \ldots\)
Hint: In part (f), write f(x) = 1/(x + 1) - 1/(x + 2).
Questions & Answers
QUESTION:
For each of the following, determine the constant c so that f(x) satisfies the conditions of being a pmf for a random variable X, and then depict each pmf as a line graph:
(a) \(f(x)=x / c, \quad x=1,2,3,4\)
(b) \(f(x)=c x, \quad x=1,2,3, \ldots, 10\)
(c) \(f(x)=c(1 / 4)^{x}, \quad x=1,2,3, \ldots\)
(d) \(f(x)=c(x+1)^{2}, \quad x=0,1,2,3\)
(e) \(f(x)=x / c, \quad x=1,2,3, \ldots, n\).
(f) \(f(x)=\frac{c}{(x+1)(x+2)}, \quad x=0,1,2,3, \ldots\)
Hint: In part (f), write f(x) = 1/(x + 1) - 1/(x + 2).
ANSWER:Step 1 of 6
(a) The pmf for a random variable X is provided as,
\(f(x)=\frac{x}{c}, \quad x=1,2,3,4\)
The value of c is computed as,
\(\begin{aligned}
\sum f(x) & =1 \\
\frac{1}{c}+\frac{2}{c}+\frac{3}{c}+\frac{4}{c} & =1 \\
\frac{10}{c} & =1 \\
c & =10
\end{aligned}\)
Thus, the value of c is 10.
The probability mass function is given as,
\(f(x)=\frac{x}{10}, \quad x=1,2,3,4\)
Steps to construct a line graph in excel are as follows,
Step 1: Enter the data in the excel sheet.