Assume that the table below represents the distribution of X. Note that X is a discrete random variable. The second column reports the number of observations for each value of X. Based on this information, what is the value of the Cumulative Distribution Function when X equals 30?
X n
20 10
25 10
30 5
15 10
10 5
To find the cumulative distribution function (CDF) when X equals 30, you need to calculate the sum of the probabilities for X less than or equal to 30.
First, let's rewrite the table to include the cumulative frequency (CF). CF represents the sum of frequencies up to a particular value of X.
X n CF
10 5 5
15 10 15
20 10 25
25 10 35
30 5 40
To calculate the CDF for X equals 30, we need to find the cumulative frequency for X equals to or less than 30. In this case, the cumulative frequency is 40, as shown in the CF column.
Next, divide the cumulative frequency by the total number of observations. In this case, the total number of observations is the sum of all frequencies, which is 40.
CDF = cumulative frequency / total observations
CDF = 40 / 40
CDF = 1
So, the value of the Cumulative Distribution Function (CDF) when X equals 30 is 1.