Let X1, X2, ... ,X9 be nine independent and identically distributed random variables from a binomial distribution with five trials and unknown probability of success. Which of the following is an unbiased estimator of p. Note that due to lack of subscripts in the answers X1 denotes X1. O (X1 + X2 +.. + X9)/45 O (X1 + X2 + ... + X9)/5 (X1 + X2 + ... + X9)/9 O X1 + X2 + ... + X9

According to recent reports, currently 39% of the population of NC (adults and children) has been fully vaccinated against Covid. Suppose of random sample of 400 individuals from the population of NC is selected. Let x represent the number in the sample who are fully vaccinated.   d. Find the probability that 130 or fewer in the sample have been fully vaccinated.  Round to 4 decimal places. Would this result be unusual? Explain.

Let X be a chi-squared random variable with 12 degrees of freedom. What is the probability that X is greater than 23? What are the steps to come to this conclusion?

What is the probability that three Poisson random independent variables A,B, C, with parameters 1, 1, 9, respectively are all equal? The answer needs to be expressed as an infinite sum of exponentials and factorials.