Random Variables
A quantitative variable that is described over a finite set of elements or a countable set of elements, even if the number of elements is infinite.
What is discrete?
Is the following a probability distribution?
x: 1 2 3 4
p(x): .23 . 32 .45 .07
What is no?
The probabilities do not add up to 1.
Binomial or not? Surveying a group of customers about their favorite cell phone.
What is no?
The mean if you play 1 ticket of the NC Pick 4 lottery each day for a year.
What is 0.0365?
How many 3-digit ID numbers are possible using digits 1 - 9 only?
What is 729?
Type of variable- The speed of a race car in mph.
What is continuous?
This is the probability model for this situation:
A box contains 3 markers, 2 pens, 1 crayon, and 1 sharpie.
Let X be the kind of writing instrument
| x: | marker | pens | crayon | sharpie |
| P(x)= | 3/7 | 2/7 | 1/7 | 1/7 |
Binomial or not? Given there are 2% purple frogs in an area, finding a purple frog.
What is yes?
The standard deviation if you play 1 ticket for the NC Pick 4 lottery each day of the year. Round to the nearest hundredth.
What is 0.19?
How many 10-digit Student ID numbers are possible if the ID has no repetitions and the digits 0 - 9 are available?
What is 10! or 3628800?
Type of variable- The number of biology majors at Halfifax Community College.
What is discrete?
Below is a probability distribution for the number of math failures of students at a school.
x: 0 1 2 3 4
P(x): .41 .38 .08 .02
Find P(x <3).
What is P(x<3)= .90
A packet of vegetable seeds has a germination rate of 96%. What is the probability that exactly 10 of 12 seeds planted will sprout?
What is .0702
In analyzing hits by V-1 buzz bombs in World War II, South London was subdivided into 576 regions, each with an area of 0.25 km2. A total of 535 bombs hit the combined area of 576 regions. If a region is randomly selected, find the probability that it was hit exactly twice.
What is 0.170?
The number of ways to select 3 individuals from a group of 15.
What is 455?
Type of variable- The height of an individual measured in inches.
What is continuous?
Find the mean for the following probability distribution:
x: 0 1 2 3 4 5 6
P(x): .04 .26 .36 .20 .08 .04 .02
What is 2.22?
The 4 conditions for using a binomial distribution.
What is
1. success/failure
2. fixed # of trials
3. events are independent
4. probability of success is constant
The four conditions for using a Poisson distribution.
What are
a) The random variable x is the number of occurrences of an event over some interval.
b) The occurrences must be random.
c) The occurrences must be independent of each other.
d) The occurrences must be uniformly distributed over the interval being used.
The number of ways to select 3 individuals from 20 if the first one selected is the leader, the second is second-in-command, and the third is the lackey.
What is 6840?
The number of individuals whose student ID starts with 012.
What is a discrete random variable?
Find the variance for the following probability distribution:
x: 0 1 2 3 4 5 6
P(x): .04 .26 .36 .20 .08 .04 .02
What is 1.5716
About 32 percent of students participate in a community volunteer program outside of school. If 30 students are selected at random, find the probability that at most 14 of them participate in a community volunteer program outside of school.
What is 0.9695?
The probability of winning the NC Pick 4 Lottery at least twice if you buy 1 ticket every day.
What is 0.00065?
The number of ways of getting a straight in poker, assume 5 cards are in your hand.
What is 10,240?