Continuous RV

Schwab

Reading

Read chapter 3.5 from Openintro statistics.

Continuous RV

  • A continuous random variable can take any numeric value.

  • (Discrete can only take integers.)

  • X- Face value of a die

  • Y- Sum of two die.

  • X and Y are discrete r.v. because their outcomes are whole numbers.

Height

X- height (inches)

X is a continuous random variable.

(people usually report is as a discrete RV.)

Tangent: Precision matters

Who is 65 inches tall?

None of us really know how tall we are exactly.

Convenience Sample on heights

Last semester my in person class told me how tall they are. I made a histogram of their heights.

Probabilities from our sample

There are 34 students in my sample (n = 34).

Treat the data as discrete.

Estimate the following probabilities.

  • P( X < 65 )
  • P( 60 < X < 63 )
  • P( X = 65 )
heights
59 61 62 63 64 65 66 67 68 69 70 71 
 1  4  3  4  6  2  2  3  2  4  2  1 

Cont. Height Density Plot

We get slightly different answers if we think about the data as continuous.

Let X - A Student’s Height

Probability Height Questions

Let’s pretend our sample is representative of all students

  • P( X < 65 )
  • P( 60 < X < 63 )
  • P( X = 65 )

Cannot be equal to exactly 1 number with continuous distributions. There is an \(\infty\) number of values.

You try.

3.37