Question

A type of robot is able to run more than one program simultaneously. The number of programs to be run varies depending on where the robot is used. A large study of robots of this type found that the distribution of the number of programs being run is summarised below. Number of programs | 1 | 2 | 3 | 4 Probability 0.5 0.25 0.15 0.1 (a) Determine the expected number of programs being run simultaneously on a randomly selected robot of this type. (3 marks) (b) Determine the standard deviation of the number of programs being run simultaneously on a randomly selected robot of this type. 3 marks) (c) For robots of this type being used with three or more programs simultaneously, give the conditional probability mass function for the number of programs being run and its mean. (4 marks

Answer 1

Answer: Given that, No of programs: probability : 2 3 4 0.5 0.25 0.15 oil Expected number of poograms. E(x) = {X. P(x) (1*0:5)+(2*0,25) +(3*0.15) + (4*0:1) = 0.5+ 0.5+ 0.45 +0.4 E(X) = 1.85 b) standard deviation of the number of programs. st.dev var (x) Here vor (x) = ECM8) - CECKT? ECS = (**0.9)+(* 0,25) +(*0.15) +(4+0.1) • 0.5t + 1.35+ 1.6 E(*2)=4.45 ..vax(x) = 4.45 - (1-852 -4.45 - 3.4225 .. Vax(x) = 1:0275 : standard deviation Frar(x) = $1.0275 = 1.0137 standard deviation: 1:0137

C) Let A be the event that 3or more programs P(X=31A)=? & P(X=41A)= ? PC X231A) - PCCX= 3)NA) 0.15 P(x=3) PCA) - 0.6 PCA) 0.15+0.1 P(X=4/A) = P{(x=4)0A) P(A) 0.1 P(X=4) PLA) 4 0.25 .: the mean 3*0.6 +4*0.4 =18+ 16 = (3.4 Thank you.