Data on the number of occurrences per time period and observed frequencies follow. Use a = .05 to perform the goodness of t test to see whether the data t a Poisson distribution. What hypotheses are appropriate for this test? Number of Occurrences Observed Frequency 0 39 l 30 2 3O 3 18 4 3 Ho: The population does not have a Poisson distribution 0 H1: The population has a Poisson distribution H0: The population has a Normal distribution 0 H1: The population does not have a Normal distribution : The population does not have a Poisson distribution Ho: The population has a Poisson distribution 0 H1: The population does not have a Poisson distribution Which of the following statements is false with respect to a Poisson distribution? . OThe Poisson distribution is an example of a discrete probability distribution. 0' . f"? The Poisson distribution is more skewed to the right for smaller values of the parameter ,u. n . "f-The Poisson distribution is symmetrical when the value of the parameter p is close to 5. D. . C' The mean of the Poisson distribution is equal to the variance. . -"\"all of these XII} 3. Given a binomial distribution with n = 10 and p = 0.2 find: a. P(x = 2) = b. P(X > 3) C. P(X = 3) Poisson Distribution: (https://stattrek.com/probability-distributions/poisson.aspx) 1. Describe the Poisson Distribution 2. Provide an example of an application of the Poisson Distribution 3. Given a Poisson Distribution with 2 = 5, find: a. P(x = 3) b. P(x >2) c. P(x= 5)27.19. [110-583:4] The moment-generating function for a random variable having a Poisson distribution with parameter A is M() = ellen) If X is the mean of a random sample of size I from a Poisson distribution with parameter 1, then which of the following statements is true? (A) X has a normal distribution with mean A and variance A. (B) X has a normal distribution with mean A and variance . (C) X has a Poisson distribution with parameter A. (D) " X has a Poisson distribution with parameter A". (E) #X has a Poisson distribution with parameter nA