Question

Given the following CDFs plot, what can you say about normal distributions: \(y_1\), \(y_2\), \(y_3\)?

  1. \(\mu_1\) > \(\mu_2\) > \(\mu_3\)
  2. \(\mu_1\) < \(\mu_2\) < \(\mu_3\)

Answer

\(\mu_1\) < \(\mu_2\) < \(\mu_3\) is correct. As for the CDFs of normal distributions, the curve is bounded between 0 and 1, as the \(\sigma\) increases the curve becomes more and more flat (towards x axis) and as the \(\mu\) increases the curve shifts more and more towards right.

As for the above question, following is the code for \(y_1\), \(y_2\) and \(y_3\):

y1 = pnorm(x, mean = -2, sd = 4)
y2 = pnorm(x, mean = 0, sd = 1)
y3 = pnorm(x, mean = 2, sd= 2.5)

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