Let f(x) be the continuous probability density function of a random variable…
2005
Let f(x) be the continuous probability density function of a random variable X. The probability that a < X ≤ b is:
- A.
f(b - a)
- B.
f(b) - f(a)
- C.
∫_a^b f(x) dx
- D.
∫_a^b x f(x) dx
Attempted by 2 students.
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Correct answer: C
For a continuous random variable X with probability density function f(x), probability is obtained by integrating the density over the required interval.
Therefore,
P(a < X ≤ b) = ∫_a^b f(x) dx.
The endpoint choice does not affect the value for a continuous distribution, because the probability at any single point is 0.