**PROPERTIES OF THE NORMAL DISTRIBUTION **

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- A normal distribution is a continuous probability distribution for a random variable.

2. The graph of a normal distribution is called the normal curve, which has all of the following properties:

- The mean, median and mode are equal.
- The normal curve is bell-shaped and is symmetric about the mean.

c. The total area under the curve is equal to one.

d. The normal curve approaches, but never touches, the x-axis.

e.The standard normal distribution is a normal distribution with a mean of 0, standard deviation of 1.

**PROPERTIES OF THE POISSON DISTRIBUTION**

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- It is named after French mathematician Siméon Denis Poisson.
- It is a discrete probability distribution.
- The Poisson distribution is popular for modelling the
*number of times an event occurs in an interval of time or space*. - Given the mean number of successes (λ) that occur in a specified region, we can compute the Poisson probability for the random variable X based on the following formula:
- The mean of the distribution is equal to λ.
- The variance is also equal to λ.

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**PROPERTIES OF THE BINOMIAL DISTRIBUTION**

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- It is a discrete probability distribution.
- A Bernoulli trial is an experiment that has exactly two outcomes. For example, the experiment of tossing a coin has two outcomes viz head or tail. One of these outcomes is called success and the other is defined as failure.
- The Binomial distribution is used to model the probability of an experiment where a Bernoulli trial is repeated multiple times. The random variable is the
*number of successes when a Bernoulli trial is repeated ‘n’ times*. - Given that a Bernoulli trial is repeated ‘n’ times with probability of success being ‘p’ and probability of failure being ‘q’, we can compute the Binomial probability for the random variable X based on the following formula: where ‘r’ is the number of successes.
- The mean of the distribution is equal to .
- The variance is also equal to .
- For p and q as defined above,

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