Generate Random Numbers Using SPSS

- Invoke SPSS
- Under the
`Data`

menu select`Insert Variable`

. Call it`v1`

. - Select
`Insert Case`

from the`Data`

menu. A missing value symbol ``.'' should appear in the first cell under variable`v1`

. Highlight that cell, copy, and paste it in 29 highlighted cells under`v1`

so that 30 empty cells will exist under`v1`

. - Under the
`Transform`

menu, select`Compute`

. In the resulting screen, put`v1`

in the box labeled`Target Variable`

. In the list of functions, scroll down and select`RV.UNIFORM`

. (Press the arrow boxes in the window with your cursor). We will generate 30 random numbers from a by means of this SPSS function. - After you clicked
`OK`

, acknowledge the`change existing variable`

warning, so that 30 numbers will appear under`v1`

. You will notice that they are decimal numbers. The uniform distribution which SPSS provides is the one for a continuous random variable. Let us generate random numbers for a discrete random variable instead as if we are tossing a fair die. - Go back to
`Compute`

in the`Transform`

menu. Put your cursor in the box where`RV.UNIFORM`

is shown and type in the box the following command:`RND(RV.UNIFORM(2,8))`

. The function`RND`

will round the uniform random numbers to produce integers. However, we need to compensate for round-off error on the end points; so type again so that you will see:`RND(RV.UNIFORM(2-.4999,8`

+`.4999))`

. Click`OK`

, acknowledge that you will overwrite the values for`v1`

to produce 30 random numbers from a U(2,8) discrete distribution. - Generate a second column of random numbers like before but call the
`Target`

`Variable`

`v2`

. - Go back to
`Compute`

in the`Transform`

menu. Put your cursor in the box where`RV.UNIFORM`

is shown and type in the box the following command:`RV.NORMAL(5,2)`

. This command will generate 30 random numbers from a distribution.Answer the following questions.

- Question 1
- : What are the expected value and variance of the discrete Uniform random variable starting at 2 and ending at 8? Hint: and
- Question 2
- : What are the sample mean and sample variance of v1?
- Question 3
- : What are the expected value and variance of the Normal random variable ?
- Question 4
- : What are the sample mean and sample variance of v2?