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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) = 5 P (X = x4). Find the probability distribution of X.

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Solution

Let P (X = x3) = k. Then,
P (X = x1) = k2

P (X = x2) = k3

P (X = x4) = k5

We know that the sum of probabilities in a probability distribution is always 1.

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

k2+k3+k+k5=115k+10k+30k+6k30=161k30=1k=3061

Now,
xi pi
x1 k2 = 1561
x2 k3 = 1061
x3 k = 3061
x4 k5= 661

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