Question

In Exercises 1–4, use the following sequence of political party affiliations of recent presidents of the United States, where R represents Republican and D represents Democrat.

R R RR D R D R RR D R RR D D R D D R R D R R D R D

Notation Identify the values of n1, n2, and G that would be used in the runs test for randomness.

Short answer

The value of\({n_1}\)is equal to 17.

The value of\({n_1}\)is equal to 10.

The value of G is equal to 16.

Step-by-step solution

Given information

A sequence of presidents from two political parties is provided.

Identify the values of \({{\bf{n}}_{\bf{1}}}{\bf{,}}{{\bf{n}}_{\bf{2}}},\;{\bf{and}}\;{\bf{G}}\)

\({n_1}\)denotes the number of Republican presidents in the sequence,that is, the number of times R occurs in the sequence.

The value of\({n_1}\)is equal to 17.

\({n_2}\)denotes the number of Democrat presidents in the sequence,that is, the number of times D occurs in the sequence.

The value of\({n_2}\)is equal to 10.

G represents the number of runs in the sequence.

A run is a sequence of similar symbols bounded by two different symbols on either side.

The number of runs in the sequence iscomputed as follows:

\(\underbrace {RRRR}_{{1^{st}}run}\underbrace D_{{2^{nd}}run}\underbrace R_{{3^{rd}}run}\underbrace D_{{4^{th}}run}\underbrace {RRR}_{{5^{th}}run}\underbrace D_{{6^{th}}run}\underbrace {RRR}_{{7^{th}}run}\underbrace {DD}_{{8^{th}}run}\underbrace R_{{9^{th}}run}\underbrace {DD}_{{{10}^{th}}run}\underbrace {RR}_{{{11}^{th}}run}\underbrace D_{{{12}^{th}}run}\underbrace {RR}_{{{13}^{th}}run}\underbrace D_{{{14}^{th}}run}\underbrace R_{{{15}^{th}}run}\underbrace D_{{{16}^{th}}run}\)

Thus, the value of G is equal to 16 runs.