Four buses carrying 152 high school students arrive to Montr

Four buses carrying 152 high school students arrive to Montreal. The buses carry, respectively, 36, 43, 35, and 38 students. One of the students is randomly selected. Let Xdenote the number of students that were on the bus carrying this randomly selected student. One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on his bus. Compute the expectations and variances of X and Y:
E(X)=
Var(X)=
E(Y)=
Var(Y)=

Solution

Consider:

Thus,      
      
E(x) = Expected value = mean =    38.25   [ANSWER]
Var(x) = E(x^2) - E(x)^2 =    10.02960526   [ANSWER]

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Thus,

          
E(Y) = Expected value = mean =    38   [ANSWER]  
Var(Y) = E(Y^2) - E(Y)^2 =    9.5   [ANSWER]