Continuous random variables

Question 1

For a continuous random variable with probability density function f, how can P(a≤x≤b) be calculated?

Answer 1

∫f(x) dx, a to b

Question 2

For a continuous random variable with probability density function f, what is ∫f(x) dx, -∞ to ∞ equal to?

Answer 2

1

Question 3

What is the relationship between a continuous random variable’s cumulative distribution function F, and its probability density function f?

Answer 3

F(x)=∫f(t) dt, -∞ to x

Question 4

For a continuous random variable with probability density function f, how can E(X) be calculated?

Answer 4

∫x*f(x) dx, -∞ to ∞

Question 5

For a continuous random variable with probability density function f, how can Var(X) be calculated?

Answer 5

(∫x²*f(x) dx, -∞ to ∞) - E(X)²

Question 6

How can the mode of a continuous random variable with probability density function f be calculated?

Answer 6

It is the global maximum of f

Question 7

How can, say, the upper quartile of a continuous random variable with cumulative distribution function F be calculated?

Answer 7

It is the value x such that F(x)=0.75