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Standard XII

Mathematics

Axiomatic Approach

The random va...

Question

The random variable X has probability distribution P(X) of the following form, where k is some number:

(a) Determine the value of k.

(b) Find P(X < 2), P(X ≥ 2), P(X ≥ 2).

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Solution

(a) It is known that the sum of probabilities of a probability distribution of random variables is one.

∴ k + 2k + 3k + 0 = 1

⇒ 6k = 1

⇒ k =

(b) P(X < 2) = P(X = 0) + P(X = 1)

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The random variable X has probability distribution P(X) of the following form, where k is some number: (a) Determine the value of k. (b) Find P(X < 2), P(X ≥ 2), P(X ≥ 2).

(a) It is known that the sum of probabilities of a probability distribution of random variables is one. ∴ k + 2k + 3k + 0 = 1 ⇒ 6k = 1 ⇒ k = (b) P(X < 2) = P(X = 0) + P(X = 1)

The random variable X has probability distribution P(X) of the following form, where k is some number:

(a) Determine the value of k.

(b) Find P(X < 2), P(X ≥ 2), P(X ≥ 2).

(a) It is known that the sum of probabilities of a probability distribution of random variables is one.

∴ k + 2k + 3k + 0 = 1

⇒ 6k = 1

⇒ k =

(b) P(X < 2) = P(X = 0) + P(X = 1)