Warm Up: 2003 AP FRQ #2. 7.1 Discrete and Continuous Random Variables. We usually denote random variables by capital letters such as X or Y When a random variable X describes a random phenomenon, the sample space S just lists the possible values of the random variable.
Here is the probability distribution for X in table form:
Find the probability that the generator produces a number X between 3 and 7
Find the probability that the generator produces a number X less than or equal to 5 or greater than 8Example
Find P(.79 < x < .81)
Find P(.799 < x < .801)
Find P(.7999 < x < .8001)
is a standard normal random variable having the distribution N(0,1).
Assume your sample proportion follows a normal distribution: N(.3, .0118).
Given: Mean = .3, and Standard dev. = .0118
Find the probability that the poll result differs from the truth about the population by more than 2 percentage points.Example
a) Identify the random variable of interest. X = ____. Then construct a probability distribution (table), and draw a probability distribution histogram.
b) Find P(X>3.5)
c) Find P(1.0 <X<3.0)
d) Find P(X<5)
2) A certain probability density function is made up of two straight-line segments. The first segment begins at the origin and goes to the point (1,1). The second segment goes from (1,1) to the point (x, 1).
a) Sketch the distribution function, and determine what x has to be in order to be a legitimate density curve.
b) Find P(0<X<.5)
c) Find P(X=1)
d) Find P(0<X<1.25)
e) Circle the correct option: X is an example of a (discrete) (continuous) random variable.