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Using the normal distribution. Let $X \sim N(1, 2)$ and $Y \sim N(2, 3)$ where $N(\mu, \sigma^2)$ denotes the normal distribution with mean $\mu$ and variance $\sigma^2$. $X$ and $Y$ are independent.

Oh sorry, I forgot to mention the work I did.I know that P(X>Y) can be translated to mean P(X-Y>0) and I want to make X-Y into one variable such as D. So P(D>0) but how do I subtract the distributions? I tried to do 1-2=-1 for the mean and then 2-3=-1 for the variance? I do not understand how this can be because we cannot take the square root of -1 to get the standard deviation. Thanks!

What is $P(X>Y)$?

Using the normal distribution. Let $X \sim N(1, 2)$ and $Y \sim N(2, 3)$ where $N(\mu, \sigma^2)$ denotes the normal distribution with mean $\mu$ and variance $\sigma^2$. $X$ and $Y$ are independent.

What is $P(X>Y)$?

I know that $P(X>Y)$ can be translated to mean $P(X-Y>0)$ and I want to make $X-Y$ into one variable such as $D$. So $P(D>0)$ but how do I subtract the distributions? I tried to do $1-2=-1$ for the mean and then $2-3=-1$ for the variance. I do not understand how this can be because we cannot take the square root of -1 to get the standard deviation.

Using the normal distribution. Let $X \sim N(1, 2)$ and $Y \sim N(2, 3)$ where $N(\mu, \sigma^2)$ denotes the normal distribution with mean $\mu$ and variance $\sigma^2$. $X$ and $Y$ are independent.

What is $P(X>Y)$?

Using the normal distribution. Let $X \sim N(1, 2)$ and $Y \sim N(2, 3)$ where $N(\mu, \sigma^2)$ denotes the normal distribution with mean $\mu$ and variance $\sigma^2$. $X$ and $Y$ are independent.

Oh sorry, I forgot to mention the work I did.I know that P(X>Y) can be translated to mean P(X-Y>0) and I want to make X-Y into one variable such as D. So P(D>0) but how do I subtract the distributions? I tried to do 1-2=-1 for the mean and then 2-3=-1 for the variance? I do not understand how this can be because we cannot take the square root of -1 to get the standard deviation. Thanks!

What is $P(X>Y)$?

Using the normal distribution. Let $X \sim N(1, 2)$ and $Y \sim N(2, 3)$ where $N(\mu, \sigma^2)$ denotes the normal distribution with mean $\mu$ and variance $\sigma^2$. X and Y are independent. Let U = 2X + 3Y .

What is $P(X>Y)$?

Using the normal distribution. Let $X \sim N(1, 2)$ and $Y \sim N(2, 3)$ where $N(\mu, \sigma^2)$ denotes the normal distribution with mean $\mu$ and variance $\sigma^2$. $X$ and $Y$ are independent.

What is $P(X>Y)$?