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We are asked to perform frequency test, serial test, and autocorrelation test on the sequence: $$ S = 0\ 1\ 1\ 0\ 0\ 1\ 1\ 1\ 0\ 0\ 0\ 0\ 1\ 1\ 0\ 0\ 1\ 0\ 0\ 1\ 1\ 1\ 0\ 0 $$ at significance level $\alpha = 0.05$. Let’s solve each step numerically. --- ### Step 1: Frequency Test (Monobit Test) 1. Count the number of 1s and 0s: * Sequence length $n = 24$ * Number of 1s ($n_1$) = 11 * Number of 0s ($n_0$) = 13 2. Compute test statistic: $$ \chi^2 = \frac{(n_1 - n_0)^2}{n} = \frac{(11 - 13)^2}{24} = ________ _________ _______ ______ _______ _______ ______ _______ __________ _________.
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