Suppose that there are four buses carrying 148 students to a math competition. The buses carry 40, 33, 25, and 50 students, respec

Suppose that there are four buses carrying 148 students to a math competition. The buses carry 40, 33, 25, and 50 students, respectively. Let X denote the number of students on the bus of a randomly chosen student. One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on the bus driven by that driver. Compute the expected values E[X] and E[Y ].

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  1. The expected value E[X] and E[Y ]
     E[X+Y] = 39.2838 + 37 = 76.2838

    What is Probability?

    The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, where, broadly speaking, 0 represents the event’s impossibility and 1 implies certainty.

    What are the 3 types of probability?

    • Classical.
    • Definition of Relative Frequency.
    • Subjective Probability.

    According to the given information :

    E(X+Y) = E(X) + E(Y)
    E[X] is the mean of X or the expected value of X.
    E[Y] is the typical or expected value for Y.
    E[X]= 40P (student in bus 1), 33P (student in bus 2), 25P (student in bus 3), and 50P (student in bus 4)
    40(40/148) + 33(33/148) + 25(25/148) + 50(50/148) = 39.2838
    E[Y] = (number of drivers)/(number of students), or 148/4, equals 37.
    So,
    E[X+Y] = 39.2838 + 37 = 76.2838
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