Let x have pmf p(x = k) = cpk k fork = 1, 2, . . where p is a parameter with 0 < p < 1 and c is a normalizing constant. we have c = −1/ log(1 − p), as seen from the taylor series − log(1 − p) = p + p2/2 + p3/3 + this distribution is called the logarithmic distribution (because of the log in the above taylor series), and has often been used in ecology.

(a) show that the pmf is a valid pmf.

(b) find the mean and variance of x.

Need now 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.

Select the correct answer. employee earnings per month($) 1 1,200 2 2,600 3 1,800 4 1,450 5 3,500 6 2,800 7 12,500 8 3,200 which measure of spread is best for the data in the table? a. range b. quartiles c. interquartile range d. mean absolute deviation

The image of abc is a'b'c. what transformations would result in this image? abc is reflected over the line x = 1, then is rotated -90° around the origin. abc is reflected over the line y = x - 1, then t: (x, y) → (x - 1, y - 1). abc is rotated 90° around the origin, then is reflected over the y-axis. abc is rotated -90° around the origin, then is reflected over the line y = -1.