Continuous Random Variables

Question 1

How do you work out k?

Answer 1

Integrate the function(s) given, with the appropriate limits. Make k the constant.

Equal it to 1, then divide 1 by whatever you found when integrating. That’s your k.

Question 2

How do you work out the mode for continuous random variables?

Answer 2

f’(x) = 0

Question 3

How do you work out the median for continuous random variables?

Answer 3

F(x) = 0.5

Question 4

How do you work out the LQ and UQ for continuous random variables?

Answer 4

Lower quartile: F(X) = 0.25

Upper quartile: F(X) = 0.75

Question 5

How do you work out the mean / E(X) for continuous random variables?

Answer 5

Use the formula in the textbook:

Integrate xf(x) dx

Question 6

How do you work out the variance for continuous random variables?

Answer 6

Use the formula booklet:

Integrate x^2 f(x) dx - mean^2

Question 7

How do you work out F(x) for Continuous Random Variables?

Answer 7

Integrate each function

Add the F(highest x value in previous function)

Question 8

How do you know if the continuous random variables are positively skewed?

Answer 8

mean > median > mode

Q3 - Q2 > Q2 - Q1

Question 9

How do you know if the continuous random variables are negatively skewed?

Answer 9

mode < median < mean

Q3-Q2 < Q2 - Q1