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Would you mind explaining the r.v from the attached photo?
Thank you
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“The monthly stock return for IBM is normally distributed with a mean of 0.08 and standard deviation of 0.04. Compute probability that the stock return = 0.05”
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Hi Will,
Really great question this one, and will definitely test people’s conceptual understanding of statistics.
What this question is really testing is people’s understanding of types of data and variables. The return of a stock is a continuous variable. This means that the accuracy of measurement can change the actual answer.
For example, if we measure to two decimal places, we could have two values that equal 0.05. However, if we measure to three, we could have 0.053 and 0.050 – these are now different answers. If we measure to 4, we could have 0.0532 and 0.0509 and so on.
The implications of this, is that we can hypothetically measure these returns to and infinite amount of decimal places, each time getting a slightly different answer. What this means for the chances of returning one specific value (in this case 0.05000000000….), is that the probability approaches 0 – P(X = 0.05) = 0.
Instead, we measure the probability of continuous variables through cumulative probability, as we find the probability of the return being above or below a certain value, but never that value exactly. So we might instead look at the cumulative probability of the return being below 0.05 (P(X < 0.05), and this includes the infinite amount of returns that occur below this value.
In essence, if there is a continuous variable, the probability that it equal one value exactly, is 0.
Hope this helps,
Tom
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