In a Poisson Distribution, if mean = e, then P(x) is given by . | Agrigyan

Q.13

ICAR AIEEA PG Statistical Sciences 09 July 2023 (Shift 1) Paper (Q.49)

MCQ (Single Correct) +4 −1

In a Poisson Distribution, if mean = e, then P(x) is given by _______.

एक पॉइसन बंटन में, यदि माध्य = e है, तो P(x) किसके द्वारा दिया जाएगा?

exp(x - e) / x! exp(x - e) / x! Correct exp(e - x) / e! exp(e - x) / e! exp(x - e) / e! exp(x - e) / e! exp(-x - e) / x! exp(-x - e) / x!

Evaluation of Poisson formula:
For a Poisson distribution with mean $\lambda = e$:

$$P(X = x) = \frac{e^{-\lambda} \lambda^x}{x!} = \frac{e^{-e} (e)^x}{x!} = \frac{e^{x - e}}{x!} = \frac{\exp(x - e)}{x!}$$

Correct: Exactly represents $\frac{e^{-e} e^x}{x!} = \frac{\exp(x - e)}{x!}$.
Incorrect: $e!$ is undefined in the denominator and numerator exponents are inverted.
Incorrect: The denominator contains $e!$ instead of $x!$.
Incorrect: $\exp(-x - e)$ is incorrect for $e^x \cdot e^{-e}$.

पॉइसन प्रायिकता फलन का मूल्यांकन:
पॉइसन बंटन हेतु जिसका माध्य $\lambda = e$ (यूलर नियतांक) है:

$$P(X = x) = \frac{e^{-\lambda} \lambda^x}{x!} = \frac{e^{-e} \cdot e^x}{x!} = \frac{e^{x - e}}{x!} = \frac{\exp(x - e)}{x!}$$

सही: यह सूत्र $\frac{e^{-e} \cdot e^x}{x!} = \frac{\exp(x - e)}{x!}$ का सही रूपांतरण है।
गलत: हर में $x!$ के स्थान पर $e!$ दिया गया है।
गलत: हर में $e!$ अमान्य है।
गलत: घातांक $-x-e$ गलत है।

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