Chapter 5: Continuous Random Variables

0.0(0)
learnLearn
examPractice Test
spaced repetitionSpaced Repetition
heart puzzleMatch
flashcardsFlashcards
Get a hint
Hint

Probability density function

Get a hint
Hint

a statistical measure used to gauge the likely outcome of a discrete value

Get a hint
Hint

Cumulative distribution function

Get a hint
Hint

a function whose value is the probability that a corresponding continuous random variable has a value less than or equal to the argument of the function.

Card Sorting

1/22

Study Analytics
Name
Mastery
Learn
Test
Matching
Spaced

No study sessions yet.

23 Terms

1
New cards

Probability density function

a statistical measure used to gauge the likely outcome of a discrete value

2
New cards

Cumulative distribution function

a function whose value is the probability that a corresponding continuous random variable has a value less than or equal to the argument of the function.

3
New cards

Continuous probability distributions

PROBABILITY = AREA

4
New cards

Continuous probability density function

gives the relative likelihood of any outcome in a continuum occurring

5
New cards

The uniform distribution

is a continuous probability distribution and is concerned with events that are equally likely to occur.

6
New cards

Uniform Mean

๐œ‡=(๐‘Ž+๐‘) / 2

7
New cards

Uniform Standard deviation

๐œŽ=โˆš((๐‘โˆ’๐‘Ž)^2 / 12)

8
New cards

Uniform pdf

๐‘“(๐‘ฅ)=1 / ๐‘โˆ’๐‘Ž for a โ‰ค x โ‰ค b

9
New cards

Uniform cdf

P(X โ‰ค x) = ๐‘ฅโˆ’๐‘Ž / ๐‘โˆ’๐‘Ž

10
New cards

Probability density function

๐‘“(๐‘ฅ)=(1 / bโˆ’a) for ๐‘Ž โ‰ค ๐‘‹ โ‰ค ๐‘

11
New cards

Area to the Left of x**

** P(X < x) = (x โ€“ a)(1 / ๐‘โˆ’๐‘Ž)

12
New cards

Area to the Right of x**

** P(X > x) = (b โ€“ x)(1 / ๐‘โˆ’๐‘Ž)

13
New cards

Area Between c and d**

** P(c < x < d) = (base)(height) = (d โ€“ c)(1 / ๐‘โˆ’๐‘Ž)

14
New cards

Memoryless property

the independence of events or, more specifically, the independence of event-to-event times or P (X > r + t | X > r) = P (X > t) for all r โ‰ฅ 0 and t โ‰ฅ 0

15
New cards

Exponential Distribution

X ~ Exp(m) where m = the decay parameter

16
New cards

decay parameter

m = 1 / ฮผ and we write X โˆผ Exp(m) where x โ‰ฅ 0 and m > 0

17
New cards

exponential pdf

f(x) = me^(โ€“mx) where x โ‰ฅ 0 and m > 0

18
New cards

exponential cdf

P(X โ‰ค x) = 1 โ€“ e^(โ€“mx)

19
New cards

exponential mean

ยต = 1/๐‘š

20
New cards

exponential standard deviation

ฯƒ = ยต

21
New cards

exponential percentile k

k = ๐‘™๐‘›(1โˆ’๐ด๐‘Ÿ๐‘’๐‘Ž๐‘‡๐‘œ๐‘‡โ„Ž๐‘’๐ฟ๐‘’๐‘“๐‘ก๐‘‚๐‘“๐‘˜) / (โˆ’๐‘š)

22
New cards

Poisson probability

๐‘ƒ(๐‘‹=๐‘˜)=๐œ†^๐‘˜ ๐‘’^โˆ’๐‘˜ / ๐‘˜! P(X=k) with mean ฮป

23
New cards

k!

k*(k-1)(k-2)(k-3)โ€ฆ32*1