QUESTION 14 14. A random variable that has a countable number of outcomes. O Ran

Question

QUESTION 14 14. A random variable that has a countable number of outcomes. O Random Variable O Continuous Random Variable O Discrete Randome Variable O Probability distribution QUESTION 15 15. A random variable that has outcomes that are measureable but not countable. O Discrete Random Variable O Continuous Randome Variable O Random Variable O Probability distribution QUESTION 16 16. A distribution displaying all possible probabilities associated with the outcomes of a random variable. O Continuous O Probability distribution O Discrete O Random Variable

Explanation / Answer

Let us first revise some definitions

Random variable:  Is a variable whose possible values are numerical outcomes of a random phenomenon. For e.g., X: Number of heads in tossing a coin 5 times.

Discrete random variable:  Discrete random variables take on a countable number of distinct values. For example, Consider an experiment where a coin is tossed three times. If X: number of times the coin comes up heads, then X is a discrete random variable that can only have the values 0, 1, 2, 3 (from no heads in three successive coin tosses, to all heads). No other value is possible for X.

Continuous random variable:  Continuous random variables can represent any value within a specified range or interval, and can take on an infinite number of possible values. An example of a continuous random variable would be an experiment that involves measuring the amount of rainfall in a city over a year, or the average height of a random group of 25 people.

Probability distribution:  A probability distribution is a table or an equation that links each outcome of a statistical experiment with its probability of occurrence.

Question 14

A random variable that has a countable number of outcomes is a disceret random variable.

Ofcourse it is also a random variable, but this is a definition of discrete random variable. As no probability is involved, it is not a probability distribution.

Question 15

A random variable that has outcomes measurable but not countable is a continuous random variable.

Again, it is also a random variable, but the definition is of continuous random variable. If it was countable outcomes, than it would be discrete random variable. Also no probability is involved so not a probability distribution.

Question 16

A distribution displaying all possible probabilities with the possible outcomes of a random variable is a probability distribution.

They are not talking about variable at all, they are talking about a distribution with probabilites associated with all outcomes, which makes it a probability distribution.

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