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Chapter 2 demonstrations - Roll of one die x P(x 1 0.166667...

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Roll of one die x P(x) 1 0.166667 2 0.166667 3 0.166667 4 0.166667 5 0.166667 6 0.166667 Roll of loaded die x P(x) 1 0.08 2 0.166667 3 0.166667 4 0.166667 5 0.166667 6 0.25 Roll of two dice x P(x) 2 0.027778 3 0.055556 4 0.083333 5 0.111111 6 0.138889 7 0.166667 8 0.138889 9 0.111111 10 0.083333 11 0.055556 12 0.027778 1 2 3 4 5 6 0 0.2 0.4 0.6 0.8 1 Probability Distribution for the roll of one die x P(x) 1 2 3 4 5 6 0.00 0.20 0.40 0.60 0.80 1.00 Probability distribution for loaded die x P(x) 2 3 4 5 6 7 8 9 10 11 12 0 0.2 0.4 0.6 0.8 1 Probability distribution for the roll of two dice x P(x)
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Tossing a coin Independent trials 10 Probability of heads 0.5 Number of heads Probability Cumulative probability 0 0.001 0.001 1 0.010 0.011 2 0.044 0.055 3 0.117 0.172 4 0.205 0.377 5 0.246 0.623 6 0.205 0.828 7 0.117 0.945 8 0.044 0.989 9 0.010 0.999 10 0.001 1.000 1 2 3 4 5 6 7 8 9 10 11 0.000 0.050 0.100 0.150 0.200 0.250 0.300 Probability Number of heads Probability
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Arrivals (per hour) at a bank ATM Mean arrival rate 10 x Probability Cumulative probability 1 0.00 0.00 2 0.00 0.00 3 0.01 0.01 4 0.02 0.03 5 0.04 0.07 6 0.06 0.13 7 0.09 0.22 8 0.11 0.33 9 0.13 0.46 10 0.13 0.58 11 0.11 0.70 12 0.09 0.79 13 0.07 0.86 14 0.05 0.92 15 0.03 0.95 16 0.02 0.97 17 0.01 0.99 18 0.01 0.99 19 0.00 1.00 20 0.00 1.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 Probability Number of arrivals Probability
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Normal Distribution Examples: The heights of students in this class follows a normal distribution, with an average of 1.75 metres and a standard deviation of 0.25 metres.
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