# Tag Info

### Conditional PDF of bivariate normal

You have learnt in class that if $(Z_1,Z_2)\in R^n\times R^d$ is Gaussian with covariance by blocks $$\Sigma=\left[\begin{array}{cc}A&B^T\\B&C\end{array}\right]$$ then the mean of $Z_1|Z_2$ is ...
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### How to create a smooth distribution of data with specific n, min, max, mean?

I figured out a way to do this using LOGNORM.DIST() function in Excel. I believe the same method can be done with NORM.DIST() as well. This method requires trial and error. Below are two images for ...

• 28.9k
1 vote

### Why does it look like the probability exceeding 1? How do you solve this problem?

To summarize the discussion in the comments: We are after the expected probability of failure, and we compute that as $$\int_0^1 x\times 2(1-x)\,dx=\frac 13$$ Thus you expect the, randomly selected, ...
• 70.6k
Accepted

### Strange consequence of linear combination of normal distribution

You have added "independent" to your claim. But then the $Y+Y$ in your question is confusing. If $Y_1 \sim N(0,1)$ and independently $Y_2 \sim N(0,1)$ then $U=Y_1+Y_1=2Y_1 \sim N(0,4)$ ...
• 157k

### Strange consequence of linear combination of normal distribution

The result is true only when the random variables are independent.The proof is simple. Without the assumption of independence, it is clearly false. A simple counter-example is $U = Y-Y = 0$ which is ...
• 140