Question

[4 5 5 2 4 4 6 3 3 7 5 3 6 3 4 4 6 5 4 5 3 7 5 5 4 2 6 5 6 6] This is my dataset Split the dataset in two equal parts. You have 30 datavalues. If you split the data in two equal parts each part will contain 15 data values.  Call the first part Y and second part X.Draw scatter plot of the 2 datasets, X being on the horizontal axis; Assume that the first part of your dataset which we called Y is actually a sample space. Then draw the histogram for the first 15 data values; As you can see Y is a discrete variable. Please write down a probability mass function for Y. Remember the example of pmf for die rolling experiment; How many possible combinations of 2 numbers out of 15 numbers are possible? Calculate the number of all possible combinations without replacement. Remember order does not matter. What if we draw 2 numbers at random out of 15 possibilities but with replacement this time. How many possibilities are there?

Answer 1

(1)

By splitting the data set in to 15 numbers each and the first 15 is named as Y and second 15 as X

Now the data sets are

Y: 4 5 5 2 4 4 6 3 3 7 5 3 6 3 4

X: 4 6 5 4 5 3 7 5 5 4 2 6 5 6 6

(2)

Histogram of y values

By tabulating the Y values are

Y values frequency

2 1  

3 4  

4 4  

5 3

6 2

7 1      

Total 15

(3)

As per the data, the probability masses of Y

Y ; 2 3 4 5 6 7

P(y): 1/15   4/15 4/15 3/15 2/15 1/15

(4)

The number of all possible combinations of 2 numbers out of 15 numbers without replacement and the order is not a matter iis

(5)

The number of all possible combinations of 2 numbers out of 15 numbers with replacement is

15x15 = 225

(order is a matter here and all the 15 numbers are considered disticnt)