7 Flashcards
Discrete variable?
Values have jumps (not continuous)
Can you have a discrete variable over continuous sample space?
Yes
Variable X is continuous if?
range of values is a continuous subset in IR.
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} = ?
Int(B) (f(x)dx) := int(1_B (x) f(x) dx)
If probability density function, then int(IR) (f(x) dx) = ?
1
Cumulative distribution function: F_x (a) := ?
P{X <= a} = int(-oo, a) (f(x) dx)
X is uniformly distributed on [0, 2] if?
P(a <= x <= b) = F(b) - F(a)
Probability of a single point in a continuous distribution?
0
Expectation of continuous random variable: E[X] = ?
Int(-oo -> oo)( f(x) x dx)
Variance of continuous random variable: Var[X] = ?
Int(-oo -> oo)(f(x)(x - mu)^2 dx)
In continuous random variable: E[a g(x)] = ?
a E[g(x)]
How to find the midpoint of a vector?
(alpha + beta)/2