1 The discrete random variable has probability function X where is a positive constant. k a Show that (3 marks) b Find the probability distribution of (2 marks) X. The discrete random variable has probability function 2 X Find a (2 marks)  b P(–1 < 2) (1 mark) ⩽X c P(X (1 mark) > −2.3) 3 The discrete random variable has probability function X where is a positive constant. k Show that = 0.25 a (2 marks) k Two independent observations and are made of X1 X2 X. b Show that P(X1 + = 5) = 0 (1 mark) X2 c Find the complete probability function for + (3 marks) X1 X2. d Find P(1.3 + 3.2) (2 marks) X2⩽ ⩽X1 4 Amir and Ed play each other at badminton and for each game, independently of all others, the probability that Amir loses is 0.2 Find the probability that, in 9 games, Amir loses: a exactly 3 of the games, (2 marks) b fewer than half of the games. (2 marks)
1 The discrete random variable X has probability function where k is a positive constant. a Show that (3 marks) b Find the probability distribution of X. (2 marks) 2 The discrete random variable X has probability function Find a  (2 marks) b P(–1 ⩽X < 2) (1 mark) c P(X > −2.3) (1 mark) 3 The discrete random variable X has probability function where k is a positive constant. a Show that k = 0.25 (2 marks) Two independent observations X1 and X2 are made of X. b Show that P(X1 + X2 = 5) = 0 (1 mark) c Find the complete probability function for X1 + X2. (3 marks) d Find P(1.3 ⩽X1 + X2⩽ 3.2) (2 marks) 4 Amir and Ed play each other at badminton and for each game, independently of all others, the probability that Amir loses is 0.2 Find the probability that, in 9 games, Amir loses: a exactly 3 of the games, (2 marks) b fewer than half of the games. (2 marks)