7 Flashcards

1
Q

Discrete variable?

A

Values have jumps (not continuous)

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2
Q

Can you have a discrete variable over continuous sample space?

A

Yes

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3
Q

Variable X is continuous if?

A

range of values is a continuous subset in IR.

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4
Q

X is a continuous random variable if a probability density function (f = f_x on IR) exists where B C R: P{X 3 B} = ?

A

Int(B) (f(x)dx) := int(1_B (x) f(x) dx)

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5
Q

If probability density function, then int(IR) (f(x) dx) = ?

A

1

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6
Q

Cumulative distribution function: F_x (a) := ?

A

P{X <= a} = int(-oo, a) (f(x) dx)

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7
Q

X is uniformly distributed on [0, 2] if?

A

P(a <= x <= b) = F(b) - F(a)

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8
Q

Probability of a single point in a continuous distribution?

A

0

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9
Q

Expectation of continuous random variable: E[X] = ?

A

Int(-oo -> oo)( f(x) x dx)

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10
Q

Variance of continuous random variable: Var[X] = ?

A

Int(-oo -> oo)(f(x)(x - mu)^2 dx)

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11
Q

In continuous random variable: E[a g(x)] = ?

A

a E[g(x)]

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12
Q

How to find the midpoint of a vector?

A

(alpha + beta)/2

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