00:01
Hello students, it is given that the buses carry respectively 38, 46, 33 and 40 students.
00:08
So, therefore the total is 38 plus 46 plus 33 plus 40 that is equal to 157 students and note that the probability that a student was on the bus is proportional to the how many students were on the bus.
00:27
So, for example, the probabilities are 38 divided by 157 on the bus a then 46 divided by 157 on the bus b and so on and the random variable x is the number of students that were on the bus carrying these randomly selected students.
00:56
So we have to compute the expectation and the variance of x and also we have given the another variable that is y which is the number of students on his bus and also we have to calculate its expectation and the variance.
01:10
So now the expectation of x is equal to 38 into the probability is 38 divided by 157 plus for the bus b 46 into 46 divided by 157 plus 33 into 33 divided by 157 plus 40 into 40 divided by 157.
01:42
So this is equal to 39 .8026.
01:48
This is the expectation of x which is 39 .8026 then the variance of x variance of x is equal to so we know the formula for the variance is summation of x minus x bar bracket square into its probability.
02:15
So this is 38 minus expectation of x is 39 .8026 bracket square into its probability is 38 divided by 157 plus 46 minus 39 .8026 bracket square into 46 divided by 157 plus 33 minus 39 .8026 bracket square into 33 divided by 157 plus 40 minus 39 .8026 bracket square into 40 divided by 157...