Distribution Flashcards
(22 cards)
What is the other name for Continuous Uniform Distribution?
Rectangular Distribution
Why does the Continuous Uniform Distribution look like a rectangle when drawn?
The probability of success is uniform (the same)
Why are the median and the mean the same for Continuous Uniform Distribution?
It is a symmetrical distribution
What should the height of CUD be?
1 ÷ (b-a)
How do you find probability with Continuous Uniform Distribution?
The area under the portion of rectangle
What are the conditions for Binomial Distribution?
- Two outcomes - ‘Success’ or ‘Failure’
- Trials are independent
- Fixed number of trials
- Constant probability
What is the notation for Binomial?
X~B(n,p)
- n = number of set trials
- p = probability of success
How to find the mean and variance of Binomial?
Mean = np
Variance = np(1-p)
What are the properties of a Normal Distribution?
- Bell-shaped curve
- Peak of the curve at 1
- Mean and median equal
- 68% data lies 1 SD away from mean
- 95% data lies 2 SD from mean
- 99.8% 3 SD away
In a Normal Distribution, what is P(X=x)?
Always zero
Normal is continuous - can’t be exact
What is the notation for Normal?
X~N(mu,sigma²)
Mu = Pop. mean
Sigma² = Pop. variance
What is the notation for Standard Normal (Z-Distribution)?
Z~N(0,1)
Formula for Standard Normal?
z = (x-mu) ÷ sigma
Or
x = mu + (z×sigma)
Or
mu = x - (z×sigma)
What is used in place of SD when calculating for Distribution of Sample Means?
Standard Error
What is the Standard Error?
Sigma ÷ Root of n
What is the notation for Sample Means Distribution?
X bar~N(mu, [sigma²÷root of n])
What is meant by a ‘Sample mean is always and unbiased estimate for population mean’?
It is equally likely to be overestimating as underestimating
What are the conditions for Normal Approximation to the Binomial?
- n>/=20 and p≈0.5
- np >/=5 and n(1-p)>/=5
What is the notation for Normal Approximation to Binomial?
X≈Y~N(np,np(1-p))
np = mean
np(1-p) = variance
What type of data is a Binomial Distribution?
Discrete
What type of data is a Normal Distribution?
Continuous
Due to Binomial and Normal being discrete vs continuous, what must be applied to any calculation?
Continuity correction
+/-0.5
