Define the discrete random variable X by where the sample space = { 1 , 2

Define the discrete random variable X by 

where the sample space Ω = {ω₁,ω₂,ω₃},P(ω₁) = P(ω₂) = P(ω₃) = 1/3. 

Find a new probability measure P̃  such that the mean becomes E_P̃ [X] = 3.5 while the variance remains unchanged. Is P̃  unique?

Transcribed Image Text:

2 X (w) 3 4 if w=w1 if w=w₂ if w if @= @3,