a. is equal to zero
b. is at least 0.5
c. depends on the probability density function
d. is very close to 1.0
b. is at least 0.5
c. depends on the probability density function
d. is very close to 1.0
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If some process can be described by a continuous random variable, then that means that it can result in an infinite number of possible results.
One example of this could be the time it takes somebody to run a 100 meter dash. Even if the runner is pretty consistent, there will be an infinite number of possible results. Let's say, for example, that the runner always finishes sometime in between 15 and 16 seconds and that any time in that range is equally likely, i.e. a uniform distribution.
Then, what is the probability that they will take EXACTLY 15.2348659934783 seconds?
Obviously, that probability is zero because there are an infinite number of other possible outcomes that can also occur and all of their probabilities have to add up to 1.
So, normally, when we work with continuous random variables, we don't talk about the probability of a specific outcome occurring because that probability is always 0. Instead, we may talk about the probability of having a result fall within a certain range.
For example in this case, the probability of running that 100 yards in between 15.3 and 15.4 seconds would be 10% since the probability density is 1 over a range of times spanning 0.1 seconds.
One example of this could be the time it takes somebody to run a 100 meter dash. Even if the runner is pretty consistent, there will be an infinite number of possible results. Let's say, for example, that the runner always finishes sometime in between 15 and 16 seconds and that any time in that range is equally likely, i.e. a uniform distribution.
Then, what is the probability that they will take EXACTLY 15.2348659934783 seconds?
Obviously, that probability is zero because there are an infinite number of other possible outcomes that can also occur and all of their probabilities have to add up to 1.
So, normally, when we work with continuous random variables, we don't talk about the probability of a specific outcome occurring because that probability is always 0. Instead, we may talk about the probability of having a result fall within a certain range.
For example in this case, the probability of running that 100 yards in between 15.3 and 15.4 seconds would be 10% since the probability density is 1 over a range of times spanning 0.1 seconds.
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The key word is RANDOM. If the value is truly random, then ANY individual number is not favored in any manner over any other. So, that means all numbers are equally unlikely as likely, so the answer would seem to be A. So, it all depends on the RANGE of values the variable can assume. If I have 10 values, the odds of any individual value would be 1 in 10. If I have 100 values, then the odds are 1 in 100. Since you have an infinite range, odds are zero for any individual number over any other. The odds are 1 in infinity which last time I looked was undefined...
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Answer to the question is CHOICE (c)...