- How do you transform a random variable?
- How a normal variable can be transformed into standard normal variable?
- 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]/2σ^2).