• A die is rolled three times with outcomes [math]X_1[/math], [math]X_2[/math], and [math]X_3[/math]. Let [math]Y_3[/math] be the maximum of the values obtained. Show that
  [[math]] P(Y_3 \leq j) = P(X_1 \leq j)^3\ . [[/math]]
  Use this to find the distribution of [math]Y_3[/math]. Does [math]Y_3[/math] have a bell-shaped distribution?
• Now let [math]Y_n[/math] be the maximum value when [math]n[/math] dice are rolled. Find the distribution of [math]Y_n[/math]. Is this distribution bell-shaped for large values of [math]n[/math]?