Multiplication of normal distribution

Thread starter garyljc
Start date Oct 8, 2008
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Distribution Multiplication Normal Normal distribution

In summary, the formula for multiplying two normal distributions is: mean of the new distribution = mean of first distribution * mean of second distribution, and variance of the new distribution = variance of first distribution * variance of second distribution. Multiplying two normal distributions results in a new normal distribution with a shape that is a combination of the two original distributions. This resulting distribution is always normal, according to the central limit theorem, and is commonly used in statistics for calculating probabilities and making predictions. However, there are limitations and assumptions, such as the independence of the two distributions and the normality of the original distributions, that should be considered when using this method.

Oct 8, 2008

garyljc

I was wondering what owuld the outcome be if I multiply both normal distribution
eg N (5, 100 ) and M ( 10,100 )

i know the operations for addition and subtraction
but what if N.M
what do i get ?

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Oct 8, 2008

Dick

Science Advisor

Homework Helper

The product of two normal distributions is not a normal distribution (unlike for sums and differences). It's called (I think) a normal product distribution.

Oct 9, 2008

garyljc

so how would the mean and sd be ?

Related to Multiplication of normal distribution

1. What is the formula for multiplying two normal distributions?

The formula for multiplying two normal distributions is: mean of the new distribution = mean of first distribution * mean of second distribution, and variance of the new distribution = variance of first distribution * variance of second distribution.

2. How does multiplying two normal distributions affect the shape of the resulting distribution?

Multiplying two normal distributions results in a new normal distribution with a shape that is a combination of the two original distributions. The resulting distribution will have a peak at the mean of the new distribution, and the spread of the distribution will be wider than the original distributions.

3. Can the multiplication of two normal distributions result in a non-normal distribution?

No, the multiplication of two normal distributions will always result in a normal distribution. This is known as the central limit theorem, which states that the sum or product of many independent random variables will tend to have a normal distribution, regardless of the distribution of the individual variables.

4. How is the multiplication of normal distributions used in statistics?

The multiplication of normal distributions is commonly used in statistics for calculating probabilities and making predictions. It is also used in the fields of finance and economics to model the behavior of stock prices and other variables.

5. Are there any limitations or assumptions when multiplying normal distributions?

Yes, there are some limitations and assumptions when multiplying normal distributions. One assumption is that the two distributions are independent of each other. Additionally, the resulting distribution may not accurately represent the true distribution if the original distributions are not normally distributed or if the sample size is small.