There are two traffic lights on a commuter's route to and from work. Let X, be the number of lights at which the commuter must stop on his way to work, and x, be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X,, X, is a random sample of size n = 2). X1 1 P(x)0.1 0.3 0.6 H = 1.5, o = 0.45 (a) Determine the pmf of T.= X, + Xg. 1 pt) (b) Calculate T How does it relate to u, the population mean? HT. (c) Calculate oT How does it relate to o, the population variance?
There are two traffic lights on a commuter's route to and from work. Let X, be the number of lights at which the commuter must stop on his way to work, and x, be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X,, X, is a random sample of size n = 2). X1 1 P(x)0.1 0.3 0.6 H = 1.5, o = 0.45 (a) Determine the pmf of T.= X, + Xg. 1 pt) (b) Calculate T How does it relate to u, the population mean? HT. (c) Calculate oT How does it relate to o, the population variance?
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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![There are two traffic lights on a commuter’s route to and from work. Let \( X_1 \) be the number of lights at which the commuter must stop on his way to work, and \( X_2 \) be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so \( X_1, X_2 \) is a random sample of size \( n = 2 \)).
\[
\begin{array}{c|ccc}
x_1 & 0 & 1 & 2 \\
\hline
p(x_1) & 0.1 & 0.3 & 0.6 \\
\end{array}
\]
\[
\mu = 1.5, \quad \sigma^2 = 0.45
\]
(a) Determine the pmf of \( T_0 = X_1 + X_2 \):
\[
\begin{array}{c|ccccc}
t_0 & 0 & 1 & 2 & 3 & 4 \\
\hline
p(t_0) & & & & & \\
\end{array}
\]
(b) Calculate \( \mu_{T_0} \):
\[
\mu_{T_0} = \underline{\hspace{1cm}}
\]
How does it relate to \( \mu \), the population mean?
\[
\mu_{T_0} = \underline{\hspace{1cm}} \cdot \mu
\]
(c) Calculate \( \sigma^2_{T_0} \):
\[
\sigma^2_{T_0} = \underline{\hspace{1cm}}
\]
How does it relate to \( \sigma^2 \), the population variance?
\[
\sigma^2_{T_0} = \underline{\hspace{1cm}} \cdot \sigma^2
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa4e23d50-b6e1-4880-9ad9-a789799b751b%2F534f6ba4-7ef0-4397-9c00-dd2b43183438%2Fwz2qsbl_processed.png&w=3840&q=75)
Transcribed Image Text:There are two traffic lights on a commuter’s route to and from work. Let \( X_1 \) be the number of lights at which the commuter must stop on his way to work, and \( X_2 \) be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so \( X_1, X_2 \) is a random sample of size \( n = 2 \)).
\[
\begin{array}{c|ccc}
x_1 & 0 & 1 & 2 \\
\hline
p(x_1) & 0.1 & 0.3 & 0.6 \\
\end{array}
\]
\[
\mu = 1.5, \quad \sigma^2 = 0.45
\]
(a) Determine the pmf of \( T_0 = X_1 + X_2 \):
\[
\begin{array}{c|ccccc}
t_0 & 0 & 1 & 2 & 3 & 4 \\
\hline
p(t_0) & & & & & \\
\end{array}
\]
(b) Calculate \( \mu_{T_0} \):
\[
\mu_{T_0} = \underline{\hspace{1cm}}
\]
How does it relate to \( \mu \), the population mean?
\[
\mu_{T_0} = \underline{\hspace{1cm}} \cdot \mu
\]
(c) Calculate \( \sigma^2_{T_0} \):
\[
\sigma^2_{T_0} = \underline{\hspace{1cm}}
\]
How does it relate to \( \sigma^2 \), the population variance?
\[
\sigma^2_{T_0} = \underline{\hspace{1cm}} \cdot \sigma^2
\]
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