Question

y is a random variable Xhaving a continu e on wh A and B = 10 Find the probably that on a given day the amount The daily amount of coffee in d ipensed by a machine located in an coffee disposed by this machine will be a) ars b) more than her than 5 c) at least 9 4 (a) The proba Dully you )

Answer 1

Uniform distribution: Uniform distribution of the random variable X is f(x) = {b^ ASXsB lo otherwise X = the amount of coffee dispensed by machine in liters. Given that X follows Uniform distribution with A = 7 and B = 10. = Distribution of X = f(x) = = for 7 sxs 10 f(x) = {* 75xs10 <x< 10 otherwise

Now we have to find the probability that the amount of coffee dispensed by machine is atmost 8.8 liters. i.e we have to find P(X < 8.8). P(X < 8.8) = 1,f(x) dx = 1994 dx = (1,9* dx) = $(x)94 = (8.8 – 7) = 1.8 = 0.6 :: P(X < 8.8) = 0.6

b) Now we have to find the probability that the amount of coffee dispensed by machine is more than 7.4 liters but less than 8.6 liters. i.e we have to find P(7.4 < X < 8.6). P(7.4 5 X 5 8.6) = s f(x) dx = sy3 dx = (dx) = (x) = (8.6 – 7.4) = 1.2 = 0.4 :: P(7.4 < X < 8.6) = 0.4

Now we have to find the probability that the amount of coffee dispensed by machine is atleast 9.4 liters. i.e we have to find P(X > 9.4). P(X 2 9.4) = 1,250 f(x) dx = 19.44dx = ($dx) = {(x) =(10 – 9.4) = 0.2 :: P(X > 9.4) = 0.2