If X~ N(0, 1), Y~N(0, 4), Z~N(0, 25). X, Y, Z are pairwise independent. Then
Question
If X~ N(0, 1), Y~N(0, 4), Z~N(0, 25). X, Y, Z are pairwise independent. Then
Solution
It seems like you didn't provide a complete question. However, I can tell you that X, Y, and Z are normally distributed random variables with means of 0 and variances of 1, 4, and 25 respectively. The term "pairwise independent" means that any two variables from the set are independent of each other.
If you want to know the distribution of the sum of these variables, for example, we can use the properties of the normal distribution. The sum of independent normally distributed random variables is also normally distributed. The mean of the sum is the sum of the means, and the variance of the sum is the sum of the variances.
So, if W = X + Y + Z, then W is a normally distributed random variable with mean 0 + 0 + 0 = 0 and variance 1 + 4 + 25 = 30. So, W~N(0, 30).
Please provide a complete question if you need more specific information.
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