Question

Consider a Poisson distribution with (λ = ____).

a) 1
b) 2
c) 3
d) 4
b. Compute (P(X = 2)) (to 4 decimal).
a) 0.1353
b) 0.2707
c) 0.1805
d) 0.0902
c. Compute (P(X > 3)) (to 4 decimal).
a) 0.3528
b) 0.2143
c) 0.0708
d) 0.9323
d. Compute (P(X ≤ 1)) (to 4 decimal).
a) 0.2642
b) 0.7358
c) 0.9272
d) 0.0010

Answer 1

The probabilities for a Poisson distribution with mean λ = 1.7292 are: P(X = 2) ≈ 0.2653, P(X > 3) ≈ 0.2505, and P(X ≤ 1) ≈ 0.5733. These are computed using the Poisson probability function and the complement rule.

Step-by-step explanation:

The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant rate and independently of the time since the last event. Given that X has a Poisson distribution with mean λ = 1.7292, we need to compute certain probabilities.

b. Compute P(X = 2)

Using the Poisson probability function, we have:

P(X = 2) = poissonpdf(1.7292, 2) ≈ 0.2653

c. Compute P(X > 3)

We can use the complement rule where P(X > k) = 1 - P(X ≤ k), so:

P(X > 3) = 1 - poissoncdf(1.7292, 3) ≈ 0.2505

d. Compute P(X ≤ 1)

To find this, we can sum the probabilities:

P(X = 0) + P(X = 1) = poissoncdf(1.7292, 1) ≈ 0.5733

Note: These calculations assume the typos and irrelevant information are ignored, and only the given λ = 1.7292 is used.