Can someone help me with this question? Assume that we collect some i.i.d. data

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Can someone help me with this question?

Assume that we collect some i.i.d. data X_1, X_2, .., X_n, and that we plot the ordered data X_(1), X_(2), .., X_(n) on the (vertical) y-axis versus the Normal quantiles q_k = mu + sigma Phi^-1 (k/n+1), for k = 1, 2, ..., n, on the (horizontal) x-axis. Suppose that the probability plot qualitatively looks like the one shown in part (a) of Figure 1: the red diagonal segment illustrates a portion of the line y = x. How does the probability density function of each of the X_i's compare to the Normal(mu, sigma^2) probability density function? Justify your answer precisely. Answer the same question for the cases illustrated in plots (b), (c), and (d).

Explanation / Answer

a) sine graph is approximately S shaped, i can say data is approximately normally distributed

b) sine graph is S shaped, i can say data is normally distributed

c) line is rising upwards - hence data is negatively skewed

c) line is rising downwards - hence data is positively skewed

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