edcommstatistics

There are lots of uncertainties in our life: monthly revenues of a business, the number of vehicles left in a parking lot everyday, the number of phone calls we get everyday, the money we spent on watching movies every year, names of customers who will enter the queue for the teller, the colours of the cars which are going to enter a toll gate in the next one hour, whether or not the next flight is going to be late, etc.  The first three are random variables, but other three are not. Among the things that are uncertain, some are random variables, some are not.  So, what characterizes a random variable? Let’s see some definitions. A random variable is a function that associates a real number with each element in the sample space. (Walpole, 1993) A random variable is a function associated with an experiment whose values are real numbers and their occurence in the trials depends on chance. (Kreyszig, 1993) First, the value of a random variable should be real numbers. Names ar

Problems Set I: The Probability of a Single Event Sample Problem #1 An experiment consists of tossing 4 coins simultaneously, once. Find the probability that at least two heads (H) appear. Answer The sample space is S = {HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, THHT, HTTH, THTH, TTHH, TTTH, TTHT, THTT, HTTT, TTTT}. $\mid S \mid = 16$ The event is E = {HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, THHT, HTTH, THTH, TTHH} $\mid E \mid = 11$ $P(E) = \frac{\mid E \mid}{\mid S \mid} = \frac{11}{16} = 0.6875$ So, the probability that at least two heads appear is 0.6875. Sample Problem #2 Fifteen cards are numbered from 1 to 15. The experiment consists of picking at random a card from the set of cards. Find the probability of getting a card with a number which is a multiply of 3. Answer The sample space is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} $\mid S \mid = 15$ The event is E  = {3, 6, 9, 12, 15} $\mid E \mid = 5$ $P(E) = \frac{\mid E \mid}{\mid S \mid} = \frac{