I understand the birthday problem wherein the probability of 2 people having the same birthday in a room of 70 people is 99.9% but what about the probability of any person in the same room having my birthday? is it the same or is this a conditional probability problem?

## Tag Archives: Probability

## Syntax template for convolving two probability distributions

I’d appreciate some help with the syntax of the following type of problem. Once I have a template of how to do it in Mathematica, I’ll be able to expand on it and work with it, but I’m new and don’t know how to get there.

I’d like to get an expression for the sum of random variables taken from the following two distributions [or equivalently the convolution of the PDFs of them]:

1) Log ( ( negative binomial with parameters r and p) + 0.5)

2) Log normal distribution with parameters mu and sigma

So my eventual distribution would be of the sum of a random variable from (1) and a random variable from (2).

Ultimately, I’d like to get the distribution of a sum of random variables from several different distributions, but once I know how to do it for two, I should be able to extrapolate from there.

Thanks very much for any help

## Probability of multivariate normal being positive on each coordinate

How can I find the probability that each coordinate of a specified multivariate normal distribution is positive? I tried the following, which I believed should work

```
mu = {0, 0, 0};
sigma = {{2, 1, 1}, {1, 2, 1}, {1, 1, 2}};
Probability[
x > 0 && y > 0 && z > 0, {x, y, z} \[Distributed]
MultinormalDistribution[mu, sigma]]
```

Unfortunately, for the output I just get the last line from the input (with mu and sigma replaced by their actual values). I don’t see where the problem could possibly be since the matrix is positive definite. If I replace it by the identity matrix everything works fine.

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