Question

Answer if each X defined as below is a random variable or not. If X is not a random variable, try to create a random variable X' based on the outcome of X. (a) X is defined as the genders of next two consecutive births in a particular hospital. (b) X is defined as the outcome of a coin toss experiment in which a coin is tossed three times. (c) X is defined as 0 when a randomly chosen adult man living in the US has a college degree,and is defined as 5 if he does not have a college degree. (d) X denotes the trials until a success occurs in a gambling machine.

Answer 1

All the options given are random variables.

a)X is a random variable with possible outcomes (M, M), (M,F), (F,M) and (F,F).

b)X is a random variable with 2^3=8 possible outcomes, (H,H,H), (H,H,T), ..., (T,T,T).

c)X is a random variable taking values 0 and 5.

d)X is a random variable taking values from 0 to Infinity and the corresponding distribution is Geometric.