# Statistics Chapter 5 - Discrete Random Variables

### Card Set Information

 Author: honestkyle ID: 204182 Filename: Statistics Chapter 5 - Discrete Random Variables Updated: 2013-04-11 12:16:12 Tags: discrete binomial distribution stats Folders: Description: Discrete Random Variables Show Answers:
1. Random Variable
• Always numerical
• Represents the outcome of an experiment
• Can be discrete or continuous
2. Are the number of discrete random values in an experiment infinite or finite?
Finite
3. How long can a sequence be for a set of discrete random values?
Infinite
4. Are the number of continuous random values in an experiment infinite or finite?
infinite
5. What is the notation for a probability in a Discrete Probability Distribution?
f(x)
6. Why aren't values in a graphical probability distribution connected like a histogram?
The values are discrete and there are no values in between
7. What is the expected value of a discrete random value?
Mean
8. What is the mean of a discrete random variable?
The value of x expected to occur in the long run and on average
9. What is the Expected Value equation?
10. What is the Variance of a Discrete RV equation?
11. What is the Variance of a Discrete Random Variable (RV)?
Average squared deviations from the expected value
12. What are examples of binomial results?
• 0 or 1
• Pass or Fail
• true or false
• success or failure
13. Jakob Bernoulli was a contributor of what?
Calculus
14. Jakob Bernoulli is known for what?
• Ars conjectandi - The art of conjecture
• First substantial treatise on probability
15. What is ars conjectandi?
Contained theory of permutation and combination  binomial theorem, multinomial theorum
16. What are the 4 properties of a binomial experiment?
• There are n identical trials in a series
• Each trial has two mutually exclusive outcomes (heat/tails, success/failure)
• Probability of success p, is constant from trial to trial
• Outcomes are independent
17. In a Binomial Distribution, what is our interest?
The number of successes occurring in the n trials of a binomial experiment
18. If you toss a coin 10 times, what is the probability of getting exactly 5 heads?
Let x = number of successes in n trials
• x = 5, n = 10, p = 0.5
19. What is the binomial probability function?
20. What does this part mean in the binomial probability function?
Number of outcomes providing exactly x successes in n trials
21. What does this part mean in the binomial probability function?
Probability of a particular sequence of outcomes with x successes in n trials
22. What can you say about a binomial distribution with the following variables?
n = 5
p = 0.1
• The highest success rate would be 0
• The lowest success rate would be 5
• The graph is skewed right
23. What can you say about a binomial distribution with the following variables?
n = 5
p = 0.5
• The highest success values would be 2 and 3 (midpoint between 0 and 5)
• The lowest success values would be 0 and 5
• The graph is normally distributed
24. What can you say about a binomial distribution with the following variables?
n = 5
p = 0.9
• The success value would be 5
• The lowest success value would be 0
• The graph is skewed left
25. What can you say about a binomial distribution with the following variables?
n = 20
p = 0.2
• The highest success values are 3 and 4
• The lowest success values are 11 - 20
• The graph is highly skewed right
26. What can you say about a binomial distribution with the following variables?
n = 50
p = 0.5
• The highest success values would be around 25
• The lowest success values would be going out from that towards the edges
• The graph is a normal distribution
27. What is the mean equation? (Expected value)
28. What is the variance equation?
29. What is the standard deviation equation?
30. If you toss a coin 100 times, what is the expected value?
• n = 100, p = 0.5
31. If you toss a coin 100 times, what is the standard deviation?
• n = 100, p = 0.5

32. Of all small businesses, 27% are women-owned. In a sample of 200 small businesses, how many would you expect to be female-owned?
• n = 200, p = 0.27
33. Of all small businesses, 27% are women-owned. if 8 small businesses were randomly selected, what is the probability that none are female-owned?
• n = 8, p = 0.27, x = 0

34. Of all small businesses, 27% are women-owned. If 8 small businesses were randomly selected, what is the probability that half are female-owned?
• n = 8, p = 0.27, x = 4