Let X be a continuous rv with cdf 0 x 0 F(x) 4 x 1 ln 4 x 0 x 4 1 x 4 [This type of cdf is suggested in the article Variability in Measured Bedload-Transport Rates (Water Resources Bull., 1985: 3948) as a model for a certain hydrologic variable.] What is a. P(X 1)? b. P(1 X 3)? c. The pdf of X?

3.1 Ans12) (a) Mean = Sum of all values divided by the number of values. Mean = ∑ x /n = 23/5 = 4.6 In order to calculate the median, we arrange the set of numbers in increasing order: 2 2 3 6 10. As the number of observations are odd, therefore median is the third value which is 3. Median = 3. Mode is the number that occurs most frequently in the given data. In this case, 2 occurs most frequently. So, mode is 2. (b)As per the question, we add 5 to each of the data values. New data set: 7 7 8 11 15. Mean = ∑ x /n = 48/5 = 9.6 In order to calculate the median, we arrange the set of numbers in increasing order: 7 7 8 11 15. As the number of observations are odd, median is the middle value which is the third value in this case. Median = 8. Mode is the number that occurs mos