In: Math
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?
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
=7
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