Infant Mortality Infant mortality is an example of a relatively rare event that can be described by the Poisson distribution, for which the probability of x occurrences is given by Xe f(x) = x! x = 0, 1, 2, ... (a) Verify that f describes a probability distribution by showing that Es(x) = 1. (b) Calculate the expected value for f, given by Exf(x). x=0 (c) In 2014, the U.S. infant mortality rate was estimated at 6.17 per 1000 live births. Assuming that this is the expected value for a Poisson distribution, find the probability that in a random sample of 1000 live births, there were fewer than 4 cases of infant mortality. Source: Central Intelligence Agency.

Question 1.2 Consider the function  f (x) = (1/24(x^2 +1)      1 < or =  x < or = 4)          = (0      otherwise)   Calculate P (x = 3) Calculate P (2 < or =  x < or = 3)         Question 1.3 Consider the function  f (x) = (k - x/4      1 < or =  x < or = 3)          = (0      otherwise)   which is being used as a probability density function for a continuous random variable x?   a. Find the value of K b. Find P (x < or = 2.5)

An individual who has automobile insurance from a certain company is randomly selected. Let Y be the number of moving violations for which the individual was cited during the last 3 years. The pmf of Y is given. y p(y) 0 1 0.50 0.35 0.10 0.05 USE SALT 3 (a) What is the probability that among 25 randomly chosen such individuals, at least 15 have no citations? (Round your answer to three decimal places.) (b) What is the probability that among 25 randomly chosen such individuals, fewer than half have at least one citation? (Round your answer to three decimal places.) What is the probability that among 25 randomly chosen such individuals, the number that have at least one citation is between 10 and 15, inclusive? ("Between a and b, inclusive" is equivalent to (a ≤ x ≤ b). Round your answer to three decimal places.) You may need to use the appropriate table in the Appendix of Tables to answer this question.