In Alpha College, students are required to join at least one school club to get extra-curriculum activities’ marks. Suppose the following table represents the probability distribution function of the number of clubs (?) a student join: ? 1 2 3 4 ?(? = ?) 0.1 2? ? + 0.1 ? (a) Find the value of ?. (b) What is the probability that a student joins at most two clubs? (c) Find ?(?), ???(?) and ?(?).
In Alpha College, students are required to join at least one school club to get extra-curriculum activities’ marks.
Suppose the following table represents the
student join:
| ? | 1 | 2 | 3 | 4 |
| ?(? = ?) | 0.1 | 2? | ? + 0.1 | ? |
(a) Find the value of ?.
(b) What is the probability that a student joins at most two clubs?
(c) Find ?(?), ???(?) and ?(?).
(d) Suppose the membership fee is $100 per club, with the first enrolled club is free of charge. Let ? be
the total membership fee a student pay. Compute ?(?) and ?(?).
(e) What percentage of students are paying not less than $200 for the total membership fee?
(f) Write a simple paragraph (about 30 -50 words) to summarize the total membership fee a student paying
for joining school club(s) (based on the results in parts (d) and (e)).
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