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edit approved Oct 7, 2021 at 20:04
Curious student
edit approved Oct 7, 2021 at 20:04
Curious student
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Let $X$ be a random variable with a continuous and strictly increasing c.d.f. function $F$ (so that the quantile function $F^{−1}$ is well-defined). Define a new random variable $Y$ by $Y = F(X)$. Show that $Y$ hasfollows a uniform distribution on the interval $[0, 1]$.

My initial thought is that $Y$ is distributed on the interval $[0,1]$ because this is the range of $F$. But how do you show that it is uniform?

Let $X$ be a random variable with a continuous and strictly increasing c.d.f. function $F$ (so that the quantile function $F^{−1}$ is well-defined). Define a new random variable $Y$ by $Y = F(X)$. Show that $Y$ has a uniform distribution on the interval $[0, 1]$.

My initial thought is that $Y$ is distributed on the interval $[0,1]$ because this is the range of $F$. But how do you show that it is uniform?

Let $X$ be a random variable with a continuous and strictly increasing c.d.f. $F$ (so that the quantile function $F^{−1}$ is well-defined). Define a new random variable $Y$ by $Y = F(X)$. Show that $Y$ follows a uniform distribution on the interval $[0, 1]$.

My initial thought is that $Y$ is distributed on the interval $[0,1]$ because this is the range of $F$. But how do you show that it is uniform?

Edited for display. A relevant tag is added.
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edit approved May 4, 2017 at 2:19
Lella
edit approved May 4, 2017 at 2:19
Lella
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Showing that Y has a uniform distribution if Y=F(X) where F is the cdf of continuous X

Let $X$ be a random variable with a continuous and strictly increasing c.d.f. function $F$ (so that the quantile function $F^{−1} is well-defined). Define a new random variable $Y$ by $Y = F(X$F^{−1}$ is well-defined)$. Show that $Y$ has a uniform distribution on the interval $[0, 1]$. Define a new random variable $Y$ by $Y = F(X)$. Show that $Y$ has a uniform distribution on the interval $[0, 1]$.

My initial thought is that $Y$ is distributed on the interval $[0,1]$ because this is the range of $F$. But how do you show that it is uniform?

Showing that Y has a uniform distribution if Y=F(X) where F is the cdf of X

Let $X$ be a random variable with a continuous and strictly increasing c.d.f. function $F$ (so that the quantile function $F^{−1} is well-defined). Define a new random variable $Y$ by $Y = F(X)$. Show that $Y$ has a uniform distribution on the interval $[0, 1]$.

My initial thought is that $Y$ is distributed on the interval $[0,1]$ because this is the range of $F$. But how do you show that it is uniform?

Showing that Y has a uniform distribution if Y=F(X) where F is the cdf of continuous X

Let $X$ be a random variable with a continuous and strictly increasing c.d.f. function $F$ (so that the quantile function $F^{−1}$ is well-defined). Define a new random variable $Y$ by $Y = F(X)$. Show that $Y$ has a uniform distribution on the interval $[0, 1]$.

My initial thought is that $Y$ is distributed on the interval $[0,1]$ because this is the range of $F$. But how do you show that it is uniform?

added 6 characters in body
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mlc
mlc
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Let X$X$ be a random variable with a continuous and strictly increasing c.d.f. function F $F$ (so that the quantile function F^−1 is well-defined). Define a new random variable Y by $F^{−1} is well-defined). Define a new random variable $Y$ by $Y = F(X). Show that Y has a uniform distribution on the interval [0$. Show that $Y$ has a uniform distribution on the interval $[0, 1]1]$.

My initial thought is that Y$Y$ is distributed on the interval [0,1]$[0,1]$ because this is the range of F is on that interval$F$. But how do you show that it is uniform?

Let X be a random variable with a continuous and strictly increasing c.d.f. function F (so that the quantile function F^−1 is well-defined). Define a new random variable Y by Y = F(X). Show that Y has a uniform distribution on the interval [0, 1]

My initial thought is that Y is distributed on the interval [0,1] because the range of F is on that interval. But how do you show that it is uniform?

Let $X$ be a random variable with a continuous and strictly increasing c.d.f. function $F$ (so that the quantile function $F^{−1} is well-defined). Define a new random variable $Y$ by $Y = F(X)$. Show that $Y$ has a uniform distribution on the interval $[0, 1]$.

My initial thought is that $Y$ is distributed on the interval $[0,1]$ because this is the range of $F$. But how do you show that it is uniform?

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user162381
user162381
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