Question
If \( X \) is a continuous random variable, then \( P(X=4)=0 \). True Not enough information False Sometimes
Ask by Salinas Pope. in the United States
Feb 24,2025
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Answer
\( P(X = 4) = 0 \) for a continuous random variable.
Solution
For a continuous random variable, the probability that it takes on any specific value is zero. This is because the probability is defined over intervals, and the probability of any single point (an interval of zero width) is 0. Therefore, P(X = 4) = 0 for a continuous random variable.
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Simplify this solution The Deep Dive
In the realm of continuous random variables, the probability of any single point value, such as \( P(X=4) \), is always zero. This is because continuous random variables can take on an infinite number of possible values within a range, and the probability is distributed over that continuum. Nonetheless, while any specific value's probability is zero, you can assess the probability of \( X \) falling within an interval, like \( P(3 < X < 5) \), which can have a positive value. This distinction is vital in understanding how continuous distributions function!
