Let X be some continuous random number whose density function is continuous and everywhere positive: fx(x) > 0 for all x ∈ R. Let FX be the accumulation function of this distribution. Show that the distribution of the transformation FX(X) is a continuous uniform distribution on the interval (0,1). Hint: You might want to calculate the accumulation function of the random variable FX (X ). For that, it is worth thinking about what the event {FX(X) ≤ x} has to do with the event {X ≤ Fx−1(x)}, and how this relates to the accumulation function.
Let X be some continuous random number whose density function is continuous and everywhere positive: fx(x) > 0 for all x ∈ R. Let FX be the accumulation function of this distribution. Show that the distribution of the transformation FX(X) is a continuous uniform distribution on the interval (0,1). Hint: You might want to calculate the accumulation function of the random variable FX (X ). For that, it is worth thinking about what the event {FX(X) ≤ x} has to do with the event {X ≤ Fx−1(x)}, and how this relates to the accumulation function.
Let X be some continuous random number whose density function is continuous and everywhere positive: fx(x) > 0 for all x ∈ R. Let FX be the accumulation function of this distribution. Show that the distribution of the transformation FX(X) is a continuous uniform distribution on the interval (0,1). Hint: You might want to calculate the accumulation function of the random variable FX (X ). For that, it is worth thinking about what the event {FX(X) ≤ x} has to do with the event {X ≤ Fx−1(x)}, and how this relates to the accumulation function.
Let X be some continuous random number whose density function is continuous and everywhere positive: fx(x) > 0 for all x ∈ R. Let FX be the accumulation function of this distribution. Show that the distribution of the transformation FX(X) is a continuous uniform distribution on the interval (0,1). Hint: You might want to calculate the accumulation function of the random variable FX (X ). For that, it is worth thinking about what the event {FX(X) ≤ x} has to do with the event {X ≤ Fx−1(x)}, and how this relates to the accumulation function.
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
Expert Solution
Step 1
Consider X as a random variable with a continuous distribution function F.
