Math 110 - Chapter 6
QUESTIONS WITH DETAILED
VERIFIED ANSWERS
Random Variable - answer a variable whose value is a numerical
outcome of a probability experiment
discrete random variable - answer a random variable that can
take one of a finite number of distinct outcomes
examples of discrete random variables - answer 1. The number
that comes up on a roll of a dice.
2. The number of siblings a randomly chosen person has.
continuous random variables - answer random variables that can
take on any value in an interval
examples of continuous random variables - answer 1. The height
of a randomly chosen college student.
2. The amount of electricity used to light a randomly selected
classroom.
, probability distribution - answer specifies the probability for each
possible value of the random variable
Properties of a probability distribution - answer A. 0 ≤ P(x) ≤ 1 for
every possible x-value
[Every value of P(x) is between 0 and 1]
B. ΣP(x) = 1
[If you add up every P(x), you get 1]
Example: Decide if the following is a probability distribution:
x-values: 1, 2, 3, 4
P(x): 0.25, 0.65 -0.3, 0.11 - answer This is not a probability
distribution. P(x=3) = -0.3, which is not between 0 and 1.
Example: Four patients have made appointments to have their
blood pressure checked at a clinic. Let X be the number of them
that have high blood pressure. The probability distribution of X is:
x-values: 0, 1, 2, 3, 4
P(x): 0.23, 0.41, 0.27, 0.08, 0.01
(a) Find P(2 or 3)
(b) Find P(More than 1)
QUESTIONS WITH DETAILED
VERIFIED ANSWERS
Random Variable - answer a variable whose value is a numerical
outcome of a probability experiment
discrete random variable - answer a random variable that can
take one of a finite number of distinct outcomes
examples of discrete random variables - answer 1. The number
that comes up on a roll of a dice.
2. The number of siblings a randomly chosen person has.
continuous random variables - answer random variables that can
take on any value in an interval
examples of continuous random variables - answer 1. The height
of a randomly chosen college student.
2. The amount of electricity used to light a randomly selected
classroom.
, probability distribution - answer specifies the probability for each
possible value of the random variable
Properties of a probability distribution - answer A. 0 ≤ P(x) ≤ 1 for
every possible x-value
[Every value of P(x) is between 0 and 1]
B. ΣP(x) = 1
[If you add up every P(x), you get 1]
Example: Decide if the following is a probability distribution:
x-values: 1, 2, 3, 4
P(x): 0.25, 0.65 -0.3, 0.11 - answer This is not a probability
distribution. P(x=3) = -0.3, which is not between 0 and 1.
Example: Four patients have made appointments to have their
blood pressure checked at a clinic. Let X be the number of them
that have high blood pressure. The probability distribution of X is:
x-values: 0, 1, 2, 3, 4
P(x): 0.23, 0.41, 0.27, 0.08, 0.01
(a) Find P(2 or 3)
(b) Find P(More than 1)
