7

Question 1

Discrete variable?

Answer 1

Values have jumps (not continuous)

Question 2

Can you have a discrete variable over continuous sample space?

Answer 2

Yes

Question 3

Variable X is continuous if?

Answer 3

range of values is a continuous subset in IR.

Question 4

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} = ?

Answer 4

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

Question 5

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

Answer 5

1

Question 6

Cumulative distribution function: F_x (a) := ?

Answer 6

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

Question 7

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

Answer 7

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

Question 8

Probability of a single point in a continuous distribution?

Answer 8

0

Question 9

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

Answer 9

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

Question 10

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

Answer 10

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

Question 11

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

Answer 11

a E[g(x)]

Question 12

How to find the midpoint of a vector?

Answer 12

(alpha + beta)/2