Is the Length of a Nail Discrete or Continuous

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University of North Bengal

Which of the following is a discrete random variable? length of time you play in a baseball game number of nails in a box length of a car volume of water in a tank

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Which of the following is a continuous random variable? number of nails in a box volume of water in a tank number of times you catch a ball in a baseball game number of red cars in a parking lot

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in this problem we have been asked which of the given is a continuous random variable. Now recall that a continuous random variable can take on uncountable E many values. So let us consider the given options. Now the first option is the number of meals in a box. Now it is possible that there are zero nails in a box or maybe there's only one nail in the box, or maybe there are two nails in the box. Or maybe there are three nails in the box and so on. So the number of nails in a box, this will be a whole number and the set of whole numbers is countable. And since it is countable, this means that there are accountably many values that the number of nails in a box can take. And so this is not a continuous random variable. Let us consider the next one, we have the volume of water in a tank. Now the volume of water in a tank, there could be absolutely no water at all. In which case the volume will be zero unit cubes. And um it's possible for the volume to be any other positive number which means that the volume of water in the tank will be any number in this interval from zero to infinity. That is, it can be any non negative number and an interval of this form can take on uncountable. E actually an interval of this form is uncountable intervals are uncountable and because of this, this means that the volume of water in the tank. This variable can take on Uncountable many values. And because of this, this is a continuous random variable. So the second option is the correct option. But let us have a look at the other options as well. The third option is the number of times you catch a ball in a baseball game. Now, maybe you don't catch it at all, Maybe you catch it only once. Maybe you catch it twice. Maybe you catch it thrice and so on, so it's going to be some whole number and the set of whole numbers is countable. So this is not a continuous random variable and the last option is the number of red cars in a parking lot. Maybe there are no red cars in a parking lot. Maybe there's only one red car in the parking lot. Maybe there are two red cars, Maybe there are three red cars and so on. So once again we can see that the number of red cars in a parking lot that will be some whole number. The set of whole numbers is countable. And so this is not a continuous random variable. So the second option will be the correct option. So the second option, this is the correct option, that is the volume of water in the tank. This is a continuous random variable

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