Answer to Question #316103 in Statistics and Probability for Aswani

Question

1. State whether the following statements are True or False and also give the reason in support of your answer.

(a)Standard deviation of a random variable X may take any real value, i.e. its value lies in the interval (-infinity, infinity)

(b)If events E1,E2,...En are mutually exclusive and exhaustive then P(E1UE2U....UEn)will be greater than 1/2 but less than 1.

(c)If X is a random variable having range set {0, 1, 2, 3} then the set {0,1,2,3} then the set {x belongs to S:X(x)=0}is an event having at least one outcome of the random experiment

Answer 1

a: no, it cannot be negative

b: no, this probability is 1

c: yes, if it has no outcomes, its probability is 0, and it cannot be in the range of random variable