What Independent random variables is
Independent random variables are variables with no connection between them. They are not related to each other in any way, and the outcome of one variable does not affect the other.
Steps for Independent Random Variables:
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Identify the two random variables to be tested for independence.
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Determine the probability distribution of each random variable.
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Calculate the joint probability of the two random variables.
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Compare the joint probability to the product of the individual probabilities for each variable.
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If the joint probability is equal to the product of the individual probabilities, then the variables are independent.
Examples
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Consider a scenario wherein a survey is conducted to gauge public opinion on a particular political issue. Each respondent’s opinion is an independent random variable.
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A study is conducted to measure the effect of a new drug on patients with a specific type of cancer. The response of each patient to the drug is an independent random variable.
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An experiment is conducted to measure the effects of different levels of light on the growth of a particular plant species. Each individual plant’s growth rate is an independent random variable.