Let X be a random variable which assumes values x1, x2, x3

1.	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» Given 2P(X = x₁) = 3P(X = x₂) = P(X = x₃) = 5P(X = x₄) = k \(\displaystyle\sum^4_{i=1} p(X = x_i) = 1\) ⇒ P(X = x₁) + P(X = x₂) + P(X = x₃) + P(X = x₄) =1 ⇒ \(\frac k2 + \frac k3 + k+\frac k5 = 1\) ⇒ \(\frac{15k + 10 k+ 30k + 6k}{30} = 1\) ⇒ \(k = \frac{30}{61}\) P(X = x₁) = \(\frac{15}{61}\) P(X = x₂) = \(\frac{10}{61}\) P(X = x₃) = \(\frac{30}{61}\) P(X = x₄) = \(\frac{6}{61}\)

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»

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

\(\displaystyle\sum^4_{i=1} p(X = x_i) = 1\)

⇒ P(X = x₁) + P(X = x₂) + P(X = x₃) + P(X = x₄) =1

⇒ \(\frac k2 + \frac k3 + k+\frac k5 = 1\)

⇒ \(\frac{15k + 10 k+ 30k + 6k}{30} = 1\)

⇒ \(k = \frac{30}{61}\)

P(X = x₁) = \(\frac{15}{61}\)

P(X = x₂) = \(\frac{10}{61}\)

P(X = x₃) = \(\frac{30}{61}\)

P(X = x₄) = \(\frac{6}{61}\)

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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.

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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.