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April 30th, 2013, 06:53 AM   #1
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Density of a random variable

Professor Roberto has to take an oral examination. The grading scale is as follows: 5: = best and 1: = worst. At most he only gives the note 4. Each student under review is questioned if he is a Lakers fan. The student's grade is based on his answer (is a fan / not a fan) and on the language in which he answered (not English / English): If the student is a fan of the Lakers reduces his note 2 points. If he answers in English reduces his note 1 point. These reductions are additive so the notes which can be obtained are {4,3,2,1}

Is fulfilled:
With probability 0.7 the student is not a fan of the Lakers
With probability 0.29 the student is a fan of the Lakers and speaks English
With probability 0.21 the student speaks English but is not a fan of the Lakers

Let N be the random variable indicating the student note. Calculate the density of N.
Can anyone help me? How/Where should I start doing this exercises? What does density mean?
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