Continuous Random Variables

Question 1

what is the usual symbol / format for the probability density function (pdf)

Answer 1

f(x)

Question 2

what is the usual symbol / format for the cumilative distribution function (cdf)

Answer 2

F(x)

Question 3

what is F(x) to X

Answer 3

F(x) is the cumilative probability function (cpf) of X

Question 4

what is the formula for getting the cumilative distribution function of f(x)

Answer 4

• the integration of f(x) = F(x)

Question 5

what do you need to remember when doing this integration

Answer 5

• you need to use dummy variables for the x in f(x) and F(x)

- because your limits are already x and infinity

Question 6

how do you get the probability density function from F(x)

Answer 6

the differentiation of F(x) = f(x)

Question 7

what is the formula for the probability of F(a) which is the cumilative probability function of X

Answer 7

F(a) = P(X <= a)

Question 8

what is P(c <= X <= d) in its cdf form

Answer 8

F(d) - F(c)

Question 9

what is the equation for working out the median of a pdf

Answer 9

• the integration of f(x) = 1/2

- then solve for x

Question 10

what is the formula for E(X) regarding pdf

Answer 10

E(X) = integration of [x * f(x)] with limits

Question 11

what is the formula of Var(X) regarding pdf

Answer 11

Var(X) = integration of {[x^2 * f(x)] - E(X)^2} with limits

Question 12

what is the usually forgotten step when working out F(x) from the integration of f(x), other than actually setting the curly brackets up for F(x) too

Answer 12

• working out c after you have integrated for F(x)
• you do this by picking the lowest value of x for when the area should = 0 and solving for c
• or picking the highest of x for when the area should be 1