Chapter 8 True & False
A continuous random variable is one that can assume an uncountable number of values.
True
If a point y lies outside the range of the possible values of a random variable X, then f(y) must equal zero.
True
A continuous random variable X has a uniform distribution between 5 and 25 (inclusive), then P(X = 15) = 0.05.
False
A probability density function shows the probability for each value of X.
False
A continuous probability distribution represents a random variable having an infinite number of outcomes which may assume any number of values within an interval.
True
A continuous random variable X has a uniform distribution between 10 and 20 (inclusive), then the probability that X falls between 12 and 15 is 0.30.
True
If X is a continuous random variable on the interval [0, 10], then P(X = 5) = f(5) = 1/10.
False
To be a legitimate probability density function, all possible values of f(x) must be non-negative.
True
Continuous probability distributions describe probabilities associated with random variables that are able to assume any finite number of values along an interval.
False
The sum of all values of f(x) over the range of [a, b] must equal one.
False
If X is a continuous random variable on the interval [0, 10], then P(X > 5) = P(X 5).
True
In practice, we frequently use a continuous distribution to approximate a discrete one when the number of values the variable can assume is countable but large.
True
Let X represent weekly income expressed in dollars. Since there is no set upper limit, we cannot identify (and thus cannot count) all the possible values. Consequently, weekly income is regarded as a continuous random variable.
True
Since there is an infinite number of values a continuous random variable can assume, the probability of each individual value is virtually 0.
True
To be a legitimate probability density function, all possible values of f(x) must lie between 0 and 1 (inclusive).
True
We distinguish between discrete and continuous random variables by noting whether the number of possible values is countable or uncountable.
True
A continuous random variable X has a uniform distribution between 5 and 15 (inclusive), then the probability that X falls between 10 and 20 is 1.0.
True