Q.Which of the following can be a valid probability distribution of a discrete random variable $X$ taking the values $0, 1, 2$?
(A) $P(0)=0.5,\ P(1)=0.3,\ P(2)=0.3$
(B) $P(0)=0.2,\ P(1)=0.3,\ P(2)=0.5$
(C) $P(0)=-0.1,\ P(1)=0.6,\ P(2)=0.5$
(D) $P(0)=0.4,\ P(1)=0.4,\ P(2)=0.4$

Birth year takes countable whole-number values, so it is discrete.

A discrete variable assumes only isolated, countable values, whereas a continuous variable can take any value in an interval. Height, weight and blood pressure of a student are measured on a continuous scale, so they are continuous. The **birt …

The maximum temperature during a day is a continuous variable, because it can take any value in an interval — option (c).

GSEB Class-12 Statistics, Random Variable chapter:

• A discrete variable takes isolated (usually whole-number) values obtained by counting.
• A continuous variable can take any value within a range and is obtained by measurement.

Checking the options:

• Number of accidents — a count → discrete.
• Number of rainy days — a count → discrete. …

A discrete random variable takes only countable (finite or countably infinite), isolated values.

A random variable is a real-valued function defined on the sample space of a random experiment. It is called a discrete random variable when the set of values it can assume is countable — either finite or countably infinite — and the values are distinct and separated (e.g. the number of heads in tosses of a coin, the number of defective items in a lot). Between two …

Birth year takes only isolated whole-number values, so it is a discrete variable; height, weight and blood pressure are continuous.

Reasoning. A discrete variable can assume only specific separated values (usually counts), while a continuous variable can take any value in an interval. Height, weight and blood pressure can take any value on a …