A school class of 120 students is driven to a symphonic concert on one of three buses. There are 34 students on one bus, 42 on another, and 44 on the third bus. When the buses arrives, one of the 120 students is randomly chosen. Let X denote the number of students on the bus of the randomly chosen student, and nd E[X]. Required:
a. What is the state space of X?
b. What is the probability mass function associated with X?
c. What is the expected value of X: E[X]?

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let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: