Binomial and Poisson Distributions

Binomial & Poisson Distributions (बाइनॉमियल और पॉइसन वितरण):-

Binomial Distribution (बाइनॉमियल वितरण):- The Binomial distribution is a discrete probability distribution that models the number of successes in a fixed number of independent trials of a binary experiment. Each trial in this experiment has two possible outcomes: "success" (usually denoted by p) and "failure" (denoted by = 1−q = 1−p).

[बाइनॉमियल वितरण एक विविक्त प्रायिकता वितरण है, जो एक निश्चित संख्या में स्वतंत्र परीक्षणों में सफलताओं की संख्या को मॉडल करता है। प्रत्येक परीक्षण में दो संभावित परिणाम होते हैं: "सफलता" (p) और "विफलता" (= 1−q = 1 - p]

Key Characteristics (मुख्य विशेषताएँ):-

i. Fixed Number of Trials (परीक्षणों की निश्चित संख्या) (n):- The number of trials (or experiments) is fixed.

[परीक्षणों की संख्या (या प्रयोग) निश्चित होती है।]

ii. Two Possible Outcomes (दो संभावित परिणाम):- Each trial results in a success or a failure.

(प्रत्येक परीक्षण का परिणाम या तो सफलता या विफलता होता है।)

iii. Constant Probability (नियत प्रायिकता) (p):- The probability of success is the same in every trial.

(सफलता की प्रायिकता प्रत्येक परीक्षण में समान होती है।)

iv. Independent Trials (स्वतंत्र परीक्षण):-

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