Topic 3: Random Variables Andn Probability Distributions Flashcards
What is the area under the curve equal to
1
Uniform distribution use and formula
Reflects all outcomes in a range having equal probabilities
P(x)= 1/b-a
Mean of uniform distribution
Mean=a+b/2
standard deviation of uniform distribution
=root of :((b-a) squared /12)
When to use uniform vs normal distribution
If it says uniform- 1/b-a
If it says normal find Z-value
X-mean/standard deviation
What is a standard normal distribution
Mean of 0, SD of 1
Empirical/normal rule (AGAIN)
68% lie within 1 SD of the mean
95% lie within 2 SD of the mean
99.7% lie within 3 SD of the mean
Chebyshev’s theorem and formula
The proportion that lie within in k standard deviations of the mean is at least 1-1/k squared.
Shown by…
K=2 at least 75% lie within 2 SD from mean
K=3 at least 89% lie within 3 SD from mean
K=4 at least 94% lie within 4 SD from mean
Uniform distribution probability formula if c and d lie within a and b
P(c<x<d)=1/b-a (d-c)
Exponential distribution definition and formula
Shows times between events
λ=1/μ
μ (rate)
Poisson distribution vs exponential distribution
Number of events happening in the period of time defimed by a rate U.
Exponential distribution is the interval between events (lander=1/U)
Exponential distribution for P(x)
P(x)= λexp(-λX)
Mean of exponential distribution
Standard deviation of exponential distribution
Both 1/ λ
Exponential distribution when finding a probability e.g time less than x (t<x) COMPARED TO time>x (t>x)
P(t<x)=1-exp(-λX)
P(t>x)=exp(-λX)