Let X be a discrete random variable with a probability mass function

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Question

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).

math Statistics-And-Probability

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Answer 1

Answer #1

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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Answer 2

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