Question

Which of the following is not true statement? a.)The value of a random variable could be zero. b.)Random variable can only have one value. c.)The probability of the value of a random variable could be zero. d.)The sum of all the probabilities in a probability distribution is always equal to one.​

Answer 1

D.the sum of all the probabilities in a probability distribution is always equal to one

Answer 2

From the given options, "b.)Random variable can only have one value" is not true.

• A variable in an equation can satisfy the equation such that its value is zero. So, it is possible that the value of a random variable is zero.
• A random can have a single value but it is not necessary that it only has one value. For example, the square root of a number can have two values, positive and negative.
• It is possible that the probability of a value of a random variable is zero. This would mean that the event cannot occur.
• When we add up the probabilities of all the events that occur in a distribution, it is equal to 1.