Suppose X is Poisson distributed with parameter 

lambdaλequals=2.02.0. 

Find the probability that X is at least 

22.

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Part 1

​P(Xgreater than or equals≥22​)equals=enter your response here




To find the probability that \( X \) is at least 2, where \( X \) follows a Poisson distribution with parameter \(\lambda = 2.0\), we want to calculate \( P(X \geq 2) \).

The Poisson distribution probability mass function (PMF) is given by:

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

To find \( P(X \geq 2) \), we can use the complement rule:

\[
P(X \geq 2) = 1 - P(X < 2)
\]

where

\[
P(X < 2) = P(X = 0) + P(X = 1)
\]

Let's calculate these probabilities and then find \( P(X \geq 2) \).The probability that \( X \) is at least 2, given that \( X \) follows a Poisson distribution with \(\lambda = 2.0\), is approximately **0.594**.

Would you like more details on this calculation or have any other questions?

Here are 5 related questions that might interest you:

1. How does the value of \(\lambda\) affect the shape of a Poisson distribution?
2. What is the probability that \( X \) is exactly 2 in this distribution?
3. How would you calculate \( P(X \leq 2) \) for the same distribution?
4. What is the expected value and variance of a Poisson distribution?
5. How can Poisson distributions be used to model real-world events?

**Tip:** When working with Poisson distributions, the complement rule is often a useful shortcut to calculate cumulative probabilities like \( P(X \geq k) \).

Learn how to calculate the probability that a Poisson-distributed random variable X is at least 2, given λ = 2.0. Explore the Poisson distribution PMF and the complement rule for probabilities with a step-by-step solution.

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