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3. According to an expert, the inflation rate and the cash rate (the interest rate set by the Reserve Bank of Australia) in A
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Answer #1

here from given distribution below is joint distribution function:

y
x 1% 2% 3% Total
1.25% 0.1500 0.1000 0.0000 0.2500
1.50% 0.1500 0.3000 0.0500 0.5000
1.75% 0.1000 0.1000 0.0500 0.2500
Total 0.4000 0.5000 0.1000 1.0000

expected value of cash rate =E(X)= ΣxP(x)=1.25*0.25+1.50*0.5+1.75*0.25=1.5

expected value of inflation rate =E(Y)=ΣyP(y)=1*0.4+2*0.5+3*0.1=1.7%

expected value of inflation rate conditional on cash rate being 1.50%

=E(Y|X=1.5)=Σy*P(Y|X=1.5)=1*(0.15/0.5)+2*(0.3/0.5)+3*(0.05/0.5)=1.8 %

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