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If X~ N(0, 1), Y~N(0, 4), Z~N(0, 25). X, Y, Z are pairwise independent. Then X+Y+Z ~ N(0, 64)X+Y+Z ~ N(0, 29)X+Y+Z ~N(0, 30)X+Y+Z~ N(0,50)

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If X~ N(0, 1), Y~N(0, 4), Z~N(0, 25). X, Y, Z are pairwise independent. Then X+Y+Z ~ N(0, 64)X+Y+Z ~ N(0, 29)X+Y+Z ~N(0, 30)X+Y+Z~ N(0,50)
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Solution 1

The sum of independent normal random variables is also a normal random variable. The mean of the sum is the sum of the means, and the variance of the sum is the sum of the variances.

Given that X, Y, and Z are independent normal random variables with means 0 and variances 1, 4, and 25 respectively Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.

Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI  is a powerful AI-powered study tool designed to help you to solve study problem.
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