The probability distributions for 2 variables are defined as followsX ~ N(120,sigma^2) and Y ~ N(mu,2sigma^2) and P(X<124) = P(Y>124. Calculate mu.

Lisa Hardin

Lisa Hardin

Answered question

2022-07-23

The probability distributions for 2 variables are defined as followsX ~ N ( 120 , σ 2 ) and Y ~ N ( μ , 2 σ 2 ) and P ( X < 124 ) = P ( Y > 124. Calculate μ .

Answer & Explanation

yermarvg

yermarvg

Beginner2022-07-24Added 19 answers

Let W := ( X 120 ) / σ , Z := ( Y μ ) / ( σ 2 ) so Z , W N ( 0 , 1 ) and
P ( W < 4 / σ ) = P ( Z > ( 124 μ ) / ( σ 2 ) ) = P ( Z < ( μ 124 ) / ( σ 2 ) ) .
Hence
4 σ = μ 124 σ 2 μ = 124 + 4 2 .

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