probability mass function and cumulative distributive function

alexia111

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in the case of a coin toss for three times, we have cases like getting 0 head, 1 head, 2 head and 3 head we calculate PMF accordingly ... but what should be the case for this question ... whether should we calculate the probability of student that stay in each year or students that leave college each year?
...
The number of students admitted to college A as freshmen is 1000 and on average 15% of the students drop every year of college (assume all degrees take 4
years).
(a) Plot the Probability Mass Function (PMF) and Cumulative Distribution Function (CDF) of the random variable corresponding to year in college of a student (Hint: X = (1, 2, 3 ,4).

i solved : 15% of 1000 = 150 leaves in first year so p(1) = (150 / 1000)
similarly now 15 % of 850 = 127.5 so p(2) = 127.5/850

is this the correct way ?
 
That looks fine. Why do you doubt?

because while solving it gets like this ...

1st year = 150/1000 = .15
2nd year = 127.5/850 = .15
3rd year = 108.375/722.5 = .15
4th year = 92.11/614.125 = .15

but the sum of PMF must be always equal to 1 .. here it is not ... and how to sove for CDF ?
 
That's actually very good. You have the right decrement for each year, but your denominators are just the previous year, They should all be 1000.

Another way of looking at it would be...

r = 1 - 0.15 = 0.85

Start: 1000
Year 1 remaining: 1000 * r
Year 2 remaining: 1000 * r^2
Year 3 remaining: 1000 * r^3

See how they all start at 1000?

This still isn't the CDF. The CDF considers ONLY those who drop out. You need to figure out how to ignore those who actually graduate.
 
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