We are interested in fitting a model with a parametric pdf equal to f_w(x) = (2x/w² , for 0 x w, 0, otherwise, where the parameter w is nonnegative.

(a) The observed values are 1.25, 0.4, 1.5, 1, 1.2. What are the possible values of the parameter w?

(b) Compute the likelihood function corresponding to these data and sketch it.

(c) What is the maximum likelihood estimate of w?

(d) If we observe 100 independent samples that are generated according to the parametric model with a fixed value of w, do you think that there is any chance that the ML estimate of w is correct? Justify your answer intuitively.

(e) Let us assume w = 2. Generate a sample from a random variable following the model using a uniform sample from the interval [0, 1] equal to 0.64.