Answer:
Cov ( X, Y ) = 1/2
Step-by-step explanation:
X = Number of heads in the first 4 flips
Y = Number of heads in the last 4 flips
Given that X and Y are binomial variables hence
P( probability ) = 1/2
Find Cov( X; Y )
xi = result of the ith flip ∴ X = x1 + x2 + x3 + x4
yj = result of the jth flip ∴ Y = y3 + y4 + y5 + y6
covariance of xi and yi = 1/2 * 1/2 = 1/4 when i = j and it is = 0 when i ≠ j
hence Cov( X; Y ) can be expressed as
Cov( X; Y ) = ∑[tex]_{i}[/tex]^4 ∑[tex]_{j}[/tex]^6 ∴ Cov( Xi , Yj ) = 2/4 = 1/2 ( given that i = j )
