Let X have density function fX(x) = ( 2x 0 < x < 1 0 otherwise and let Y be uniformly distributed on the interval (0, 1). Assume X and Y are independent. (a) Find the density function of X + Y . Hint: Start by finding the CDF of X + Y and be careful. (b) Calculate the probability P(X + Y ≥ 3/2).

Tracy solved the following problem. which of the statements is true? 9 ÷ 3 + 6 × 2 3 + 6 × 2 9 × 2 18 her answer is correct. her answer is incorrect. she should have multiplied before dividing. her answer is incorrect. she should have multiplied before adding. her answer is incorrect. she should have added before dividing.

What is the logarithmic function modeled by the following table? x f(x) 9 2 27 3 81 4

Max recorded the heights of 500 male humans. he found that the heights were normally distributed around a mean of 177 centimeters. which statements about max’s data must be true? a) the median of max’s data is 250 b) more than half of the data points max recorded were 177 centimeters. c) a data point chosen at random is as likely to be above the mean as it is to be below the mean. d) every height within three standard deviations of the mean is equally likely to be chosen if a data point is selected at random.