Question:
In a Poisson Distribution, if mean = e, then P(x) is given by ____________.
In a Poisson Distribution, if mean = e, then P(x) is given by ____________.
Show Hint
Always start by writing down the general formula and then substitute the given parameters. Simplifying using basic exponent rules easily reveals the matching option.
Updated On: Jul 24, 2026
- $\exp(x-e)/x!$
- $\exp(e-x)/e!$
- $\exp(x-e)/e!$
- $\exp(-x-e)/x!$
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
The Poisson distribution is a discrete probability distribution that models the number of events occurring in a fixed interval of time or space.
Key Formula or Approach:
The probability mass function of a Poisson distribution with parameter (mean) $\lambda$ is: \[ P(X = x) = \frac{e^{-\lambda} \lambda^x}{x!}, \quad x = 0, 1, 2, \dots \]
Step 2: Detailed Explanation:
Given that the mean of the distribution is: \[ \lambda = e \] Substitute $\lambda = e$ into the Poisson probability mass function: \[ P(X = x) = \frac{e^{-e} e^x}{x!} \] Combine the exponential terms in the numerator using exponents laws ($e^a \cdot e^b = e^{a+b}$): \[ P(X = x) = \frac{e^{x-e}}{x!} \] Rewriting this in functional notation: \[ P(X = x) = \frac{\exp(x-e)}{x!} \]
Step 3: Final Answer:
The derived probability mass function is $\exp(x-e)/x!$, which matches Option (A).
The Poisson distribution is a discrete probability distribution that models the number of events occurring in a fixed interval of time or space.
Key Formula or Approach:
The probability mass function of a Poisson distribution with parameter (mean) $\lambda$ is: \[ P(X = x) = \frac{e^{-\lambda} \lambda^x}{x!}, \quad x = 0, 1, 2, \dots \]
Step 2: Detailed Explanation:
Given that the mean of the distribution is: \[ \lambda = e \] Substitute $\lambda = e$ into the Poisson probability mass function: \[ P(X = x) = \frac{e^{-e} e^x}{x!} \] Combine the exponential terms in the numerator using exponents laws ($e^a \cdot e^b = e^{a+b}$): \[ P(X = x) = \frac{e^{x-e}}{x!} \] Rewriting this in functional notation: \[ P(X = x) = \frac{\exp(x-e)}{x!} \]
Step 3: Final Answer:
The derived probability mass function is $\exp(x-e)/x!$, which matches Option (A).
Was this answer helpful?
0
0
Top ICAR AIEEA Statistical Science Questions
- Which is called as the brain of the nematode?
- If an exporter earns money and deposits that with Reserve Bank of India (RBI), what will be the ultimate impact on country's money supply?
- Anthracnose resistant variety of French bean is:
- The process of assembling, storage, grading, packaging and distribution of different agricultural products is known as ...........
- What is the working principle of a potometer?
View More Questions
Top ICAR AIEEA Probability Questions
- Two unbiased dice are thrown simultaneously. Then the possible number of outcomes will be:
- If $C_1$ and $C_2$ are subset of sample space S. Then which is correct:
- Two dice are rolled simultaneously. What is the probability that the sum of numbers on dice is 9?
- Given \(P(A) = p_1, P(B) = p_2\) and \(P(AB) = p_3\). Then \(P(A' \cap B')\) will be:
- If \(X\) is a random Poisson variate with \(P(X=1) = P(X=2)\). Then \(P(X=4)\) is:
View More Questions
Top ICAR AIEEA Questions
- Which of the following statements is false?
- Which of the following is an example of an inventory?
- According to Adam Smith, productivity gains could be brought about through .
- The supply curve for an artificially scarce good is .
- Which of the following would not be considered an opportunity cost of paid employment?
View More Questions