Let X be a discrete random variable with a probability mass function
Let X be a discrete random variable with a probability mass function (pmf) of the following quadratic form: p(x) = Cx(5 – x), for x = 1,2,3,4 and C > 0.
(a) Find the value of the constant C.
(b) Find P(X ≤ 2).
Homework Answers
a) We compute the value of C by using the property that the sum of all probabilities have to be equal to 1. Therefore, we have here:
P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 1
4C + 6C + 6C + 4C = 1
20C = 1
C = 1/20 = 0.05
Therefore C = 0.05 is the required value here.
b) The required value here is computed as:
P( X <= 2) = P(X = 1) + P(X = 2) = 4C + 6C = 10C = 0.5
Therefore 0.5 is the required value here.
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