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Let X and Y be two independent random variables with the moment gener.pdf

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sayanhaldar1999

Let X and Y be two independent random variables with the moment generating functions MX(t)=1t+t2+1(t)(>0.5) and MY(t)=1+t+t2+2(t), where t0limi(t)=0, t0limi(k)(t)=0 for i=1,2 and k=1,2,3 (i.e., these functions 1(t),2(t) and their first three derivatives converge to zero as t0). Define Z=X+Y. Find the maximum value of skewness of Z. Find the variance Var(Z) of Z with maximum skewness..

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Let X and Y be two independent random variables with the moment generating functions MX(t)=1t+t2+1(t)(>0.5) and MY(t)=1+t+t2+2(t), where t0limi(t)=0, t0limi(k)(t)=0 for i=1,2 and k=1,2,3 (i.e., these functions 1(t),2(t) and their first three derivatives converge to zero as t0). Define Z=X+Y. Find the maximum value of skewness of Z. Find the variance Var(Z) of Z with maximum skewness.

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Let X and Y be two independent random variables with the moment gener.pdf

  • 1. Let X and Y be two independent random variables with the moment generating functions MX(t)=1t+t2+1(t)(>0.5) and MY(t)=1+t+t2+2(t), where t0limi(t)=0, t0limi(k)(t)=0 for i=1,2 and k=1,2,3 (i.e., these functions 1(t),2(t) and their first three derivatives converge to zero as t0). Define Z=X+Y. Find the maximum value of skewness of Z. Find the variance Var(Z) of Z with maximum skewness.