Question

2. A total of 4 buses carrying 148 students from the same school arrive at a football stadium. The buses carry, respectively, 40, 33, 25, and 50 students. One of the students is randomly selected. Let X denote 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 her bus. (a) Which of E[X] or E[Y] do you think is larger? Why? (b) Compute the expected value of X and the expected value of Y. (c) Compute the standard deviations of X and Y.

Answer 1

Gfven, X40,33,250-> Y PCY)4 148 PCX 33)33 48 PCK25)=25 148 PCK50) 48 PCY40)P(4=33)= pC1=25)=p (1=50) a expect ELK) to be bigge init s Per-Student ather than avevage the Per-bu bExpected Value af x 40 oug33215 EtK) 39.28 Erpected Valuu Ho 33 25J+s0(

ECY) 37 c Standard deviation af x EnowsDVaante we Vanan te x) x)-(eck)) 33 33 1625.42 ccx)-(ex) --1.18) Varianu Cx) 1625. 42- 82-S0 . SDCX) 82-So -7.08 deviation of y Stardard €cy2) -- ECY) Vaian e () 148 1453.5 Variane Cy)4 53-5-(3) S.D C 4.S 9.19
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