Public interest in becoming an English teacher is very high. They are willing to take the TOEFL test many times to become English teachers. The following is data on the number of participants and the frequency with which they took the TOEFL test in New Delhi in 2017

Frequency of taking the test	Number of participants
1	721,769
2	601,325
3	166,736
4	22,299
5	6,730

a. Suppose X is a random variable that shows the frequency of participants taking the TOEFL test. Show the probability distribution of X b. What is the probability that a participant takes the test more than once? c. What is the average frequency of participants taking the TOEFL test d. What is the variance and standard deviation of the frequency of participants taking the TOEFL test