The binomial random variables are obtained as the sum of iid Gaussian trials.

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The correct answer is False.

A binomial random variable is a random variable that counts the number of successes in a sequence of independent experiments each of which yields success with probability $p$. A Gaussian random variable, also known as a normal random variable, is a random variable with a probability distribution that is bell-shaped.

The sum of iid Gaussian trials is a Gaussian random variable. However, the sum of iid binomial trials is not necessarily a Gaussian random variable. For example, if $X$ is a binomial random variable with parameters $n$ and $p$, then the

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sum of $n$ independent copies of $X$ is a binomial random variable with parameters $n^2$ and $p^2$. This is not a Gaussian random variable unless $p=0$ or $p=1$.

In conclusion, the binomial random variables are not obtained as the sum of iid Gaussian trials.

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