What did you learn from binomial and Hyper- geometric distributions? Write a brief note of five lines on these distributions

 

Q# What did you learn from binomial and Hyper- geometric distributions?  Write a brief note of five lines on these distributions.                                                       

Answer

A binomial distribution can be thought of as simply the probability of a SUCCESS or FAILURE outcome in an experiment or survey that is repeated multiple times. The binomial is a type of distribution that has two possible outcomes (the prefix “bi” means two, or twice). For example, a coin toss has only two possible outcomes: heads or tails and taking a test could have two possible outcomes: pass or fail.

For example, let’s suppose we wanted to know the probability of getting a 1 on a die roll. if you were to roll a die 20 times, the probability of rolling a one on any throw is 1/6. Roll twenty times and you have a binomial distribution of (n=20, p=1/6). SUCCESS would be “roll a one” and FAILURE would be “roll anything else.” If the outcome in question was the probability of the die landing on an even number, the binomial distribution would then become (n=20, p=1/2). That’s because your probability of throwing an even number is one half.

The hypergeometric distribution is a discrete distribution that models the number of events in a fixed sample size when you know the total number of items in the population that the sample is from. Each item in the sample has two possible outcomes (either an event or a nonevent). The samples are without replacement, so every item in the sample is different. When an item is chosen from the population, it cannot be chosen again. Therefore, an item's chance of being selected increases on each trial, assuming that it has not yet been selected.

Use the hypergeometric distribution for samples that are drawn from relatively small populations, without replacement. For example, the hypergeometric distribution is used in Fisher's exact test to test the difference between two proportions, and in acceptance sampling by attributes for sampling from an isolated lot of finite size.

The hypergeometric distribution is defined by 3 parameters: population size, event count in population, and sample size.

For example, We receive one special order shipment of 500 labels. Suppose that 2% of the labels are defective. The event count in the population is 10 (0.02 * 500). we sample 40 labels and want to determine the probability of 3 or more defective labels in that sample. The probability of 3 of more defective labels in the sample is 0.0384.