(Solved): 5. Four balls, numbered \( 0,1,2,3 \) are placed in an urn. Two balls are randomly selected (withou ...

5. Four balls, numbered \( 0,1,2,3 \) are placed in an urn. Two balls are randomly selected (without replacement) from the four, and their numbers are noted. Let the random variable \( \mathrm{X} \) be the largest of the two selected numbers. Write the probability distribution for \( \mathrm{X} \) (in the form of a table). Also, let the random variable \( \mathrm{Y} \) be the absolute value of the difference of the two selected numbers. Write the probability distribution for \( \mathrm{Y} \) (in the form of another table). [Hint: First write the sample points of the experiment of selecting two balls from the four.] 6. Let \( Y \) be a random variable with the following probability distribution: \( \mathrm{p}(\mathrm{y})=\mathrm{y} / 6 \) for \( \mathrm{y}=1 ; 2 ; 3 \) and ( 0 otherwise). Write the probability distribution for \( \mathrm{Y} \) in the form of a table. Find \( \mathrm{E}(\mathrm{Y}), \mathrm{V}(\mathrm{Y}) \), and \( \mathrm{E}\left(Y^{3}-1\right) \)