Figure 3
Central limit theorem. On the left are the probability distributions showing the bias of the six-sided die (shown with dots) and on the right the histogram of 10 000 trials of the average of 40 rolls of the die. If the probability distribution is continuous rather than discrete (shown on the right with a line connecting the dots), the distribution of the average is also continuous (shown with Gaussian function over the histogram). (a) Unbiased die: the distribution of the average is a Gaussian with μ = 3.5 and σ = 0.27. (b) Linearly biased die: the distribution of the average is a Gaussian with μ = 4.3 and σ = 0.24. (c) Quadratically biased die: the distribution of the average is a Gaussian with μ = 4.8 and σ = 0.19. |