If X1 and X2 are normally independently distributed random v

If X1 and X2 are normally independently distributed random variables with a mean 10 and the variance 16, what is the probability that 3X1-X2 is less than 10 or greater than 30?

Mean of 3X1-X2 = 3*10-10 = 20

Variance of 3X1-X2 = 9*16+16 = 160

As the range is symmetrical around 20, we convert this to the standard normal distribution.

Z= (30-20)/40 = 1/4 = 0.25

The corresponding probability = 0.4

Therefore, the two sided probability for the same would be 2*0.4 = 0.8

If X1 and X2 are normally independently distributed random variables with a mean 10 and the variance 16, what is the probability that 3X1-X2 is less than 10 or

If X1 and X2 are normally independently distributed random v

Solution

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