Modal value or most probable value

4 Each of the variables \(W , X , Y\) and \(Z\) takes eight integer values only. The probability distributions are illustrated in the following diagrams. \includegraphics[max width=\textwidth, alt={}, center]{43f7e091-9ae7-4373-a209-e2ebdba5260f-3_437_394_397_280} \includegraphics[max width=\textwidth, alt={}, center]{43f7e091-9ae7-4373-a209-e2ebdba5260f-3_433_380_397_685} \includegraphics[max width=\textwidth, alt={}, center]{43f7e091-9ae7-4373-a209-e2ebdba5260f-3_428_383_402_1082} \includegraphics[max width=\textwidth, alt={}, center]{43f7e091-9ae7-4373-a209-e2ebdba5260f-3_425_376_402_1482}

1. For which one or more of these variables is
   1. the mean equal to the median,
   2. the mean greater than the median?
   3. Give a reason why none of these diagrams could represent a geometric distribution.
   4. Which one of these diagrams could not represent a binomial distribution? Explain your answer briefly.

14 A counter is initially at point \(O\) on the \(x\)-axis. A fair coin is thrown 6 times. Each time the coin shows heads, the counter is moved one unit in the positive \(x\)-direction. Each time the coin shows tails, the counter is moved one unit in the negative \(x\)-direction. The final distance of the counter from \(O\), in either direction, is denoted by \(D\). Determine the most probable value of \(D\). \section*{END OF QUESTION PAPER} \section*{OCR
Oxford Cambridge and RSA}

1 The discrete random variable \(X\) has probability distribution function $$\mathrm { P } ( X = x ) = \begin{cases} 0.45 & x = 1 \\ 0.25 & x = 2 \\ 0.25 & x = 3 \\ 0.05 & x = 4 \\ 0 & \text { otherwise } \end{cases}$$ State the mode of \(X\) Circle your answer.
0.25
0.45
1
2.5

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. [1 mark] 0.1 \quad 0.25 \quad 2 \quad 3