Question

Let a pair of dice be thrown and the random variable X be the sum of the numbers that appear on the two dice. Find the mean or expectation of X. Select the correct answer from above options

Answer 1

let x be the sum of numbers on the two dice x=2;p(2)= 1 36 x=3;p(3)= 2 36 x=4;p(4)= 3 36 x=5:p(5)= 4 36 x=6;p(6)= 5 36 x=7;p(7)= 6 36 x=8;p(8)= 5 36 x=9;p(9)= 4 36 x=10;p(10)= 3 36 x=11;p(11)= 2 36 x=12;p(12)= 1 36 mean = ∑xp(x) = 2 36 +3⋅ 2 36 +4⋅ 3 36 +5⋅ 4 36 +6⋅ 5 36 +7⋅ 6 36 +8⋅ 5 36 +9⋅ 4 36 +10⋅ 3 36 +11⋅ 2 36 +12⋅ 1 36 = 252 36 =7 answer