Topic 3: Random Variables Andn Probability Distributions Flashcards

1
Q

What is the area under the curve equal to

A

1

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2
Q

Uniform distribution use and formula

A

Reflects all outcomes in a range having equal probabilities

P(x)= 1/b-a

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3
Q

Mean of uniform distribution

A

Mean=a+b/2

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4
Q

standard deviation of uniform distribution

A

=root of :((b-a) squared /12)

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5
Q

When to use uniform vs normal distribution

A

If it says uniform- 1/b-a

If it says normal find Z-value

X-mean/standard deviation

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6
Q

What is a standard normal distribution

A

Mean of 0, SD of 1

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7
Q

Empirical/normal rule (AGAIN)

A

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

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8
Q

Chebyshev’s theorem and formula

A

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

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9
Q

Uniform distribution probability formula if c and d lie within a and b

A

P(c<x<d)=1/b-a (d-c)

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10
Q

Exponential distribution definition and formula

A

Shows times between events

λ=1/μ

μ (rate)

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11
Q

Poisson distribution vs exponential distribution

A

Number of events happening in the period of time defimed by a rate U.

Exponential distribution is the interval between events (lander=1/U)

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12
Q

Exponential distribution for P(x)

A

P(x)= λexp(-λX)

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13
Q

Mean of exponential distribution

Standard deviation of exponential distribution

A

Both 1/ λ

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14
Q

Exponential distribution when finding a probability e.g time less than x (t<x) COMPARED TO time>x (t>x)

A

P(t<x)=1-exp(-λX)

P(t>x)=exp(-λX)

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