Given that x has a Poisson distribution with muequals1.8​, what is the probability that xequals2​?
Question content area bottom
Part 1
​P(2​)almost equals
  
enter your response here ​(Round to four decimal places as​ needed.)

The Poisson probability formula is given by:

\[
P(X = k) = \frac{e^{-\mu} \cdot \mu^k}{k!}
\]

Where:
- \( \mu = 1.8 \) (the mean of the distribution),
- \( k = 2 \) (the value we're interested in).

Let's plug in the values to calculate \( P(X = 2) \):

\[
P(X = 2) = \frac{e^{-1.8} \cdot 1.8^2}{2!}
\]

Now, I will compute this.

The probability that \( X = 2 \) for a Poisson distribution with \( \mu = 1.8 \) is approximately \( 0.2678 \).

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. What is the probability that \( X = 0 \) for \( \mu = 1.8 \)?
2. How would the probability change if \( \mu = 2.5 \)?
3. What is the cumulative probability \( P(X \leq 2) \) for this distribution?
4. How does the Poisson distribution differ from the normal distribution?
5. Can you compute the mean and variance of the Poisson distribution?

**Tip:** The mean and variance of a Poisson distribution are both equal to \( \mu \).

Given that x has a Poisson distribution with mu equals 1.8, what is the probability that x equals 2? (Round to four decimal places as needed.)

Learn how to calculate the probability that X equals 2 for a Poisson distribution with a mean (mu) of 1.8. This detailed solution walks through the Poisson probability formula step-by-step, ideal for students in Grades 10-12. Round to four decimal places as needed.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation