If \( X \) is a continuous random variable, then \( P(X=4)=0 \). True Not enough information False Sometimes
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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!
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