Question

Most computer languages include a function that can be used to generate random numbers. In Excel, the RAND function can be used to generate random numbers between 0 and 1. If we let x denote a random number generated using RAND, then x is a continuous random variable with the following probability density function. for 0 sxs 1 elsewhere (a) Graph the probability density function. f(x) f(x) EEEEEEEEEEEEE Endas tiers - 3 - Terce BOORTE E segments Egertice Tesegent o tickereler ertica is line 1 (b) What is the probability of generating a random number between 0.15 and 0.75? (c) What is the probability of generating a random number with a value less than or equal to 0.10? (d) What is the probability of generating a random number with a value greater than 0.807 (e) Generate 50 random numbers by entering = RAND() into 50 cells of an Excel worksheet. This answer has not been graded yet. (f) Compute the mean and standard deviation for the random numbers in part (e).

Answer 1

Answer: The given pdf is f(0) = 1 - OLX elsewhere (a) the prob-density function graph is flac) Y + a random (b) The probability of generating number between 0.15 and 0.75 p(0.152840.75) = s idx 0-75 0.15 0.75 ab 10.15 = 0.75- 0.15 TP(0.152X40-75) = 0.61 Thus, the probability generating random number between 0.15 and 0.95 is o.6 . The probability of generating a random with a value less than or equat to a value number with 0.10

0.10 p(x20.10) = f f(x) doc = solda = [2].0-10. = 0.10-0 Plxc0:10) 20.10 Thus, probability of generating random numbers with a value less than or equal to 0.80 PS Colo. (d) The probability of generating a random number with a value greater than 0.80. P(x > 0.80) = $a f(a) dx 030 = Side 020 = [X36380 = 1-0,80 P(x>0.80) 20:20 Thus, the probability number with a value of genewating random greater than 0.8ots 0.20.