A random sample of 80 observations of the continuous random variable X was taken and the values

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A random sample of 80 observations of the continuous random variable X was taken and the values are summarised in the following table.


It is required to test the goodness of fit of the distribution having probability density function f given by


a. Show that the expected frequency for the interval 2 ≤ x < 3 is 40 and calculate the remaining expected frequencies.

b. Carry out a goodness of fit test, at the 10% significance level.

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