Suppose that X₁, X₂, X3 are mutually independent random variables with the respective momen generating functions, Mx, (t) = ²², Mx₂ (t) = e²t + 3t², and Mx, (t) = (-¹) ². ez

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Suppose that X₁, X2, X3 are mutually independent random variables with the respective moment
generating functions, Mx, (t) = et², Mx, (t) = ²t + 3t², and Mx, (t) = (-)².
a) Calculate the probability that X₂ is between 2 and 4, P(2 <X₂ < 4).
b) State with parameter(s) the probability distribution of Y = X₁ + X₂.
Transcribed Image Text:Suppose that X₁, X2, X3 are mutually independent random variables with the respective moment generating functions, Mx, (t) = et², Mx, (t) = ²t + 3t², and Mx, (t) = (-)². a) Calculate the probability that X₂ is between 2 and 4, P(2 <X₂ < 4). b) State with parameter(s) the probability distribution of Y = X₁ + X₂.
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