Question

Task The Stanley Cup Finals is a best of seven championship series for the National Hockey League (NHL). The frequency table displays the number of games played each year between 1939 and 2019. Please note that the Stanley Cup Finals did not take place in the 2004-2005 season due to an NHL lockout. 4 *(games played) Frequency 20 5 19 6 23 7 17 a. (2pts)Define the random variable X in this scenario. b. (10pts)Build a probability distribution for the random variable. Show that the criteria for a valid distribution have been met. c. (5pts)Compute the expected value of the random variable. Interpret the value in context. d. (3pts) What is the probability 6 games are played in the Stanley Cup finals? e. (5pts) What is the probability no more than 6 games are played in the Stanley Cup Finals? C

Answer 1

1. 
   26 19. 6 (al Answer consider the frequency table xe (gamer played) frequency(fi) Relative freq (Yi= fill Efi) 4 (120179 = 0.2532 0.2405 5 W 19179 = 23 231795 0.2911 7 17 17179 0.2152 Total 79 Eri=1 The random variable x is defined as the number of games played in a "Stanley Cup finals series between year 1939 and 2019, (6) The probability distribution for 8.v. x is Х :4 51 20179 P(X=Xų 19179 23179. 17179 19 Ś P(X=X) = 20+ 23 I since =1 79 79 So it is a valid distribution. 6 17 + + 79 4
   
   7. +5819 24 79 79 The expected value of rivox is Elx= [X PLX=X) = 4 x 20 23 6x + + .7 x 17 79 .79 1.0127 +1.2025 +1.7.468 + 1.5063 5.4683 So the expected value of x is 5.4683, that means on an querage, each year in a series, 5.4683 games playes between 1939 and 2019. d) The probability that 6 games are played in the Stanley Cup finals is P(x=67= 0.2911 les The prob that no more than 6 games played in the Stanley Cup finals in Plx56)= |- P(x=7) = l- 17 62 79 = 0.7848 79 23 79 G3