1.

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.

Answer» 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 = `sum x p(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`
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