A Random Variable X ~ N (0, 1). Find P(X > 0) and P(X < 0). - Mathematics and Statistics

A random variable X ~ N (0, 1). Find P(X > 0) and P(X < 0).

Solution

Given X ∼ N(0, 1)

∴ μ = 0

∴ P(X > μ) = P(X > 0) = 1/2 as the distribution is symmetric about μ = 0.

P(X < μ ) = P(X < 0) = 1/2 as the distribution is symmetric about μ = 0.

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