2023 Stats3 Discrete Random Variables BMQ solutions (RVHS)

Statistics 3 Tutorial: Discrete Random Variables Basic Mastery Questions 1. Two fair dice are thrown. Let X be the sum of the two results. By considering the 36 possible outcomes, (i) make a table of probability distribution. (ii) find P( 4)X  . (iii) Calculate the mean of the random variable of X. Solution: (i) X = x 2 3 4 5 6 7 8 9 10 11 12 P(X = x) 1 36 2 36 3 36 4 36 5 36 6 36 5 36 4 36 3 36 2 36 1 36 (ii) 30 5( 4) ( 5) 36 6P X P X     (iii) ( ) ( ) 2 6 12 20 30 42 40 36 30 22 12 36 36 36 36 36 36 36 36 36 36 36 7 E X xP X x               2. A bag contains eight blue discs and seven orange ones. Two discs are removed without replacement. Given that X is the number of orange discs taken out , draw up a probability distribution table, showing all the values of X together with the probability of each occurrence. Solution: X = x 0 1 2 P(X = x) 8 7 56.15 14 210 8 7 1122. .15 14 210 7 6 42.15 14 210