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