BSTAT Ch6
probability density function
F(x) for a continuous random variable has the following properties * f(x) ≥ 0 for all possible values x of X, and * the area under f(x) over all values of x equal one
For a continuous random variable X, How many distinct values can it assume over an interval?
Infinite
The lognormal distribution is defined with reference to which distribution?
The normal distribution
The probability that a continuous random variable X assumes a particular value x is
Zero
The shape of the graph depicting the normal probability density function is
bell shaped
For a continuous random variable X, the function used to find the area under f(x) up to any value x is called
cumulative distribution function
For a continuous random variable, one characteristic of its probability density function f(x) is that the area under f(x) over all values of x is
equal to one
The distinct values of both a continuous random variable and a discrete random variable can be counted
false
The expected value and variance of the standard normal random variable Z are both zero
false
Cumulative distribution function
for any value x if the random variable X, the cumulative distribution functions F(x) is define as F(x)=P(X≤x).
Continuous random variable
is characterized by uncountable values because it can take n any value within an interval or collections of intervals
A characteristic of the normal distribution is that
it is symmetric around its mean
The probability distribution of a discrete random variable is called its probability
mass function
The exponential random variable is
nonnegative
The probability distribution of a continuous random variable is called
probability density function
For data that are normally distributed, 95% of the data will fall within 2 standard deviations of that mean
true
Consider data that are normally distributed. In order to transform a standard normal value z unto its unstandardized value x, we use the following formula:
x=µ+zơ
Consider data that are normally distributed. In order to transform a value x into it standardized value z, we use the following formula
z=x-µ/ơ
A random variable X follows the continues uniform distribution if
its has an equally likely chance of assuming any value within a specified range