Identify the FALSE statement relative to a continuous random variable, x, and its probability distribution:
a. The distribution of x is modelled by a smooth curve called a probability density function.
b. P(x = a) is given by the height of the density function above the point, a.
c. The total area under the graph of the density function is 1.
d. The area above an interval and below the density curve gives the probability of x lying in that interval.
The distribution of a continuous random variable is defined by an equation called probability density function. Hence, Option A seems right here.
The area bounded by the curve of the density function and the x-axis is equal to 1, when computed over the domain of the variable. Option C seems fine too.
The probability that a random variable assumes a value between a and b is equal to the area under the density function bounded by a and b. Option D is correct as well.
Option B, which says the height of the density function above the point a defines the probability is incorrect. The probability is defined by the area covered by that point.
Option B is the answer.
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