Question

Find each specified probability below. Assume that the random variable X has a Poisson distribution with the given value of λ.

1. P (X=2), λ=1.80

2. P (X=13), λ=6.50

3. P(X<4), λ=8.30

4. P(X=0), λ=2.60

5. P (X<8), λ=2.90

Answer 1

Poisson probabilities can be calculated using the formulas: P(X = k) = poissonpdf(λ, k) and P(X ≤ k) = poissoncdf(λ, k). By substituting the given values of λ and k into these formulas, the probabilities can be easily calculated.

Step-by-step explanation:

1. To find P(X=2) when λ=1.80, we can use the formula: P(X = k) = poissonpdf(λ, k). Plugging in the values, we have P(X=2) = poissonpdf(1.80, 2) ≈ 0.2676

2. P(X=13) when λ=6.50 can be calculated using the same formula: P(X = k) = poissonpdf(λ, k). So, P(X=13) = poissonpdf(6.50, 13) ≈ 0.0136

3. To find P(X<4), we can use the formula: P(X ≤ k) = poissoncdf(λ, k). Substituting in the values, we have P(X<4) = poissoncdf(8.30, 3) ≈ 0.2386

4. To find P(X=0) with λ=2.60, we can use the formula: P(X = k) = poissonpdf(λ, k). Therefore, P(X=0) = poissonpdf(2.60, 0) ≈ 0.0728

5. To calculate P(X<8) when λ=2.90, we can use the formula: P(X ≤ k) = poissoncdf(λ, k). Plugging in the values, we have P(X<8) = poissoncdf(2.90, 7) ≈ 0.7320.