Suppose we would roll two standard 6-sided dice. (a) Compute the expected value of the sum...

Suppose we would roll two standard 6-sided dice.

(a) Compute the expected value of the sum of the rolls.

(b) Compute the variance of the sum of the rolls.

(c) If X represents the maximum value that appears in the two rolls, what is the expected value of X? What’s the probability of sum = 7?

Solutions

Expert Solution

The probability distribution

So then we compute the expected value, using

E(X)= ∑x(P(X)=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

Variance = sumation of (X- mean)²*f(x)

So then we compute the expected value, using

E(X)=∑x(P(X)=x)

         =(2-7)²⋅1/36+(3-7)²⋅2/36+(4-7)²⋅3/36+(5-7)²⋅4/36
             +(6-7)²⋅5/36+(7-7)²⋅6/36+(8-7)²⋅5/36+(9-7)²⋅4/36
             +(10-7)²⋅3/36+(11-7)⋅2/36+(12-7)²⋅1/36

=35/6

Probability of x=7 is 6/36 = 1/6

milcah answered 8 months ago

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