Question

Let X be a random variable which assumes values x₁, x₂, x₃, x₄ such that 2P(X = x₁) = 3P (X = x₂) = P (X = x₃) = 5P(X = x₄). Find the probability distribution of X.

Answer 1

Key point to solve the problem:

If a probability distribution is given then as per its definition, Sum of probabilities associated with each value of random variable of given distribution is equal to 1

i.e. ∑(p_i) = 1

Let,

2P(X = x₁) = 3P (X = x₂) = P (X = x₃) = 5P(X = x₄) = k (say)

∴ P(X = x₁) = k/2

P(X = x₂) = k/3

P(X = x₃) = k

P(X = x₄) = k/5

∵ ∑(p_i) = 1 {∵ it is given that it is a probability distribution}

15k + 30k + 10k + 6k = 30 [ by taace LCM ]

61k = 30

k = 30/61

∴ the required probability distribution is :