HW 23 (+6)Multidimensional Opinion Model 1. (+6)Let the joint distribution of two optimal policies and be given by a. (+2)What is the unconditional probability that ? When , what is the conditional...

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HW 23 (+6)    Multidimensional Opinion Model
1. (+6)    Let the joint distribution of two optimal policies and be given by
    
    
    
    
    
    
    
    
    
a. (+2)    What is the unconditional probability that ? When , what is the conditional probability that as well?
. (+4)    Find the co
elation coefficient between and . (Hint: recall that, for random variables and , , where and .)
Answered 3 days AfterApr 04, 2022

Solution

Komalavalli answered on Apr 07 2022
11 Votes
a.
    
    
    
    
    
    
the unconditional probability that
=1/8+3/8
= 4/8 =
1/2 =0.5
the unconditional probability that is 0.5
When , the conditional probability that as well
Conditional probability
    
    
    
    
When , the conditional probability that is 3/8 = 0.3
.
E(z1) = 3/8+1/8+1/8+3/8 =1
E(z12) = 3/82+1/82 +3/82+1/82
E(z12) = 0.14+0.015 +0.14+0.015 =0.31
E(z22) = 3/82+1/82 +3/82+1/82
E(z22) =...
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