S2- Continuous Random Variables

Question 1

What is the mode of a continuous random variable?

Answer 1

Value of X with the greatest frequency, which can be found out from a sketch of the function

Question 2

How can the median be worked out?

Answer 2

F(m)=0.5

Question 3

How can the quartiles be obtained?

Answer 3

F(Q1)=0.25

F(Q3)=0.75

Question 4

How is the probability density function defined?

Answer 4

x^n + x^m + etc a≤x≤b

f(x)= 0 otherwise

Question 5

E(x)=

Answer 5

∫x(f(x))

Question 6

E(x^2)=

Answer 6

∫x^2 (f(x))

Question 7

Var(x)=

Answer 7

E(x^2) - (E(x))^2

Question 8

Relationship between f(x) and F(x)?

Answer 8

F(x) is the integral of f(x)

Question 9

What is the cumulative distribution function?

Answer 9

F(X) –> P(X≤x)