Consider that X and Y are independent standard normal random variables. Find P[Y>4X]
Try to solve this problem yourself before moving on to the solution below
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As X and Y are mean 0 normal random variables, Y - 4X is also a mean 0 normal random variable. Therefore, P[Y > 4X] = P[Y - 4X > 0] is asking the probability that a normal random variable is greater than its mean. This is 0.5 by the symmetry of the normal distribution about its mean.
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