statistics

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two dices are tossed once. let the random variable be t he sum of the up faces on the dice. A). find and graph the probability distribution of the random variable. and b) calculate the mean (or expectation) of this distribution

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    X=2=1+1 (1st face + 2nd face)P=1/36
    X=3=1+2=2+1 P=2/36
    X=4=1+3=3+1=2+2 P=3/36
    X=5=1+4=4+1=2+3=3+2 P=4/36
    X=6=1+5=5+1=2+4=4+2=3+3 P=5/36
    X=7=1+6=6+1=2+5=5+2=3+4=4+3 P=6/36
    X=8=2+6=6+2=3+5=5+3=4+4 P=5/36
    X=9=3+6=6+3=4+5=5+4 P=4/36
    X=10=4+6=6+4=5+5 P=3/36
    X=11=5+6=6+5 P=2/36
    X=12=6+6 P=1/36

    Note 1/36=(1/6)*(1/6),
    1/36+2/36+3/36+4/36+5/36+6/36+
    5/36+4/36+3/36+2/36+1/36=36/36=1

    B) m(X)=2*(1/36)+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)=
    (2+6+12+20+30+42+40+36+30+22+12)/36=
    252/36=7

    We can also use the independence of numbers on two dice. The mean of the sum
    = the sum of two means: if X=X1+X2 and X1, X2 are independent then m(X1+X2)=m(X1)+m(X2)
    7=3.5+3.5

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