In a project, 5 excavators need to be used. The probability of a single excavator malfunctioning is 0.0594. And their operational functioning is independent from each other.1. Which variable should be formulated as discrete random variable?2. What is the probability that exactly 2 excavators will be malfunctioning?3. What is the probability that there are less than 3 excavators malfunctioning?4.Give 2 reasons why independency assumption might be violated?Anyone please be kind enough to clear my ignorance in the above questions. I am happy to thank you in advance
1/ X is number of faulty excavator 2/ Pr(X=2) = 5C2 (0.0594)^2 (1-0.0594)^3 = 0.0294 3/ Pr(X<3) = (0.9406)^5 + 5(0.0594)(0.9406)^4 + 0.0294 = 0.9981
1. x, for the number of excavators malfunctioning, takes on the values 0,1,2,3,4,5 p = .0594 q = 1 - p = .9406 2.. P(x=2) = 5C2* p^2 * q^3 = .02936 3. P(x<3) = P(0)+P(1)+P(2) = .73625+ .23248+ .02936 = .99809 4.Think of a reason where the malfunction of one causes problems for the others.
