The expected value of the sum of the two numbers obtained on the uppermost faces, when two fair dice are rolled, is

Step-by-step solution

In a single throw of a pair of dice, the sum of the numbers on them can be 2,3,4,5,6,7,8 , 9,10,11,12 . So X can take values 2,3,4, , 12. The probability distribution of X is aligned & E ( X ) = & x_i P (x_ i ) = & 1 36 2+ 2 36 3+ 3 36 4+ 4 36 5 & + 5 36 6+ 6 36 7+ 5 36 8+ 4 36 9 & + 3 36 10+ 2 36 11+ 1 36 12 aligned aligned & E ( X )= 1 36 (2+6+12+20+30+42+40 & E ( X )= 252 36 =7 aligned