1 The discrete random variable \(X\) has the following probability distribution function.
$$\mathrm { P } ( X = x ) = \begin{cases} 0.2 & x = 1
0.3 & x = 2
0.1 & x = 3,4
0.25 & x = 5
0.05 & x = 6
0 & \text { otherwise } \end{cases}$$
Find the mode of \(X\).
Circle your answer.
[0pt]
[1 mark]
0.10 .2523
\(2 \quad \mathrm {~A} \chi ^ { 2 }\) test is carried out in a school to test for association between the class a student belongs to and the number of times they are late to school in a week.
The contingency table below gives the expected values for the test.
| Number of times late |
| \cline { 2 - 7 }\cline { 2 - 6 } | | \(\mathbf { 0 }\) | \(\mathbf { 1 }\) | \(\mathbf { 2 }\) | \(\mathbf { 3 }\) | \(\mathbf { 4 }\) |
| \cline { 2 - 7 } | \(\mathbf { A }\) | 8.12 | 14 | 15.12 | 14 | 4.76 |
| \cline { 2 - 7 }
Class | \(\mathbf { B }\) | 8.99 | 15.5 | 16.74 | 15.5 | 5.27 |
| \cline { 2 - 7 } | \(\mathbf { C }\) | 11.89 | 20.5 | 22.14 | 20.5 | 6.97 |
Find a possible value for the degrees of freedom for the test.
Circle your answer.
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