Let X1, X2, ..., Xn be an iid random sample with parameter ẞ. Suppose that the pdf of X is the following: B f(x) x+1: 1 < x < ∞, ẞ>1 = 0, otherwise a.) Show that the expected value of X is b.) What is the Method of Moments Estimator (MOM) for ẞ? Problem #1 continued c.) What is the Maximum Likelihood Estimator (ẞMLE) for ẞ?

Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.