Probability one random variable greater than another
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Answer:Using the normal distribution. Let X∼N(1,2) and Y∼N(2,3) where N(μ,σ2) denotes the normal distribution with mean μ and variance σ2. X and Y are independent.
What is P(X>Y)?
I know that P(X>Y) can be translated to mean P(X−Y>0) and I want to make X−Y into one variable such as D. So P(D>0) but how do I subtract the distributions? I tried to do 1−2=−1 for the mean and then 2−3=−1 for the variance. I do not understand how this can be because we cannot take the square root of -1 to get the standard deviation.
Step-by-step explanation:
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