Normal

Transform random variable to normal

Transform random variable to normal
  1. How do you transform a random variable?
  2. How a normal variable can be transformed into standard normal variable?
  3. What is the formula for normal random variable?

How do you transform a random variable?

The transformation y=a+Bx maps Rn one-to-one and onto Rn. The inverse transformation is x=B−1(y−a). The Jacobian of the inverse transformation is the constant function det(B−1)=1/det(B). The result now follows from the multivariate change of variables theorem.

How a normal variable can be transformed into standard normal variable?

Any normal distribution can be converted into the standard normal distribution by turning the individual values into z-scores. In a z-distribution, z-scores tell you how many standard deviations away from the mean each value lies.

What is the formula for normal random variable?

For a random variable x, with mean “μ” and standard deviation “σ”, the normal distribution formula is given by: f(x) = (1/√(2πσ2)) (e[-(x-μ)^2]/^2).

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