Answer :

Given,



Our variable is X and from equation we see that it is taking values X = 0,1,2,3,4 …… (any whole number)


And it represents the number of colleges in which you are going to get admission.


According to equation given we have :


P(X = 0) = k×0 = 0


P(X = 1) = k×1 = k


P(X = 2) = 2k×2 = 4k


P(X = 3) = k(5-3) = 2k


P(X = 4) = k(5-4) = k


P(X>4) = 0


As in question, it is not given either X is random variable or the given distribution is a probability distribution, we can’t apply any thing directly.


But we have a hint in the question,


As P(X = 0) = 0


It means the chance of not getting admission in any college 0


admission is sure


Hence the sum of all probabilities must be equal to 1 as getting admission has become a sure event.


This makes the given distribution a probability distribution an X a random variable also.


k + 4k+2k+k = 1


8k = 1


k = 1/8


i) P(getting admission in exactly one college) = P(1) = k = 1/8


ii) P(getting admission in atmost 2 colleges) = P(X≤2)


= P(X = 1)+P(X = 2)


= k+4k = 5k = 5/8


iii) P(getting admission in atleast 2 colleges) = P(X≥2)


= P(X = 2)+P(X = 3)+P(X = 4)


= 4k+2k+k = 7k = 7/8


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