Statistics, Statistical Analysis, Random Variable, Discrete Random Variable, Mathematics.
here X is a random variable and c is constant Proof: E[cX]= ∑ ct*fₓ(t) = c ∑ t*fₓ(t) = c*E[X] Next we can see E[X+Y]= E[X]+E[Y] for any 2 random variables X and Y Proof: E[X+Y] = ∑ (t₁ + t₂) fₓᵧ(t₁,t₂) = ∑ t₁*fₓᵧ(t₁,t₂) + ∑t₂*fₓᵧ(t₁,t₂)= E[X] + E[Y] This concludes the result- E[aX+bY] = aE[X] +