Assume a Poisson distribution with λ=4.8.
Find the following probabilities
a. X=1 | b.
X<1 |
c.
X>1. |
d.
X≤1. |
a) P(X = 1)
= 0.0395
b) P(X < 1)
= P(X = 0)
= 0.0082
c) P(X > 1)
= 1 - P(X < 1)
= 1 - [P(X = 0) + P(X = 1)]
= 1 - [0.0395 + 0.0082]
= 0.9523
d) P(X < 1)
= P(X = 0) + P(X = 1)
= 0.0395 + 0.0082
= 0.0477
Assume a Poisson distribution with λ=4.8. Find the following probabilities a. X=1 b. X<1 c....
Assume a Poisson distribution. Find the following probabilities a. Let λ = 2.0, find P(X≥3). b. Let λ = 0.6, find P(X≤1) c. Let λ = 2.0, find P(X≤2)
Assume a Poisson distribution. Find the following probabilities. a. Let λ-5.0, find P(X23). b. Let λ:0.6, find P(X 1 ) c. LetA-6.0, find P(XS2) a. When A 5.0, P(X23)- Round to three decimal places as needed.) b. When λ:0.6, P(X 1,- (Round to three decimal places as needed.) C. When λ-60, P(X4- (Round to three decimal places as needed.) 1
Consider a Poisson probability distribution with λ=2.6. Determine the following probabilities. a) P(x=5) b) P(x>6) c) P(x≤3)
Assume a Poisson distribution. a. If A 2.5, find P(X-5) c. If λ-0.5, find P(X-0). b. IfX-8.0, find P(X-4) d. If 3.7, find P(X-6) a. P(X 5)- Round to four decimal places as needed.)
Assume that the variable X is distributed as a Poisson with λ = 5.7. Calculate the following probabilities. a. Pr( X = 1 ) b. Pr( X < 1 ) c. Pr( X > 1 ) d. Pr( X ≤ 1 )
Assume a Poisson distribution with-5.8. Find the following probabilities. b.X-1 с. X>1 Compute the mean and standard deviation for the following hypergeometric distributions. a. n-3, N 9, and E-7 b. n- 5, N-8, and E-3 c. n-6, N 14, and E 3 d. n 4, N-9, and E 4
The Poisson distribution with parameter λ has the mass function defined by p(x) = λ x e −λ/x! if x is a nonnegative integer (and 0 otherwise). Find the probability it assigns to each of the following sets: a. [0, 2) b. (−∞,1] c. (−∞,1.5] d. (−∞, 2) e. (−∞,2] f. (0.5, ∞) g. {0, 1, 2} Find the CDF of the uniform distribution on (0,1).
Assume a Poisson distribution. Find the following probabilities. a. Let lambda equals7.0, find P(Xgreater than or equals 3 ). b. Let lambda equals0.6, find P(Xless than or equals 1). c. Let lambda equals6.0, find P(Xless than or equals 2).
(a)Suppose X ∼ Poisson(λ) and Y ∼ Poisson(γ) are independent, prove that X + Y ∼ Poisson(λ + γ). (b)Let X1, . . . , Xn be an iid random sample from Poisson(λ), provide a sufficient statistic for λ and justify your answer. (c)Under the setting of part (b), show λb = 1 n Pn i=1 Xi is consistent estimator of λ. (d)Use the Central Limit Theorem to find an asymptotic normal distribution for λb defined in part (c), justify...
Compute the expected value of the Poisson distribution with parameter λ X ∼ Poisson(λ). Show E[X(X − 1)(X − 2)· · ·(X − k)] = λ ^(k+1) Use this result, and that in question above, to calculate the variance of X