Question

Examine whether the following distribution is a probability distribution of a discrete random variable X :
PM = \(\frac{x+2}{25}\); x = 1, 2, 3, 4, 5

Answer 1

Here, p (x) = \(\frac{x+2}{25}\)

Putting, x = 1, 2, 3, 4, 5

P(1) = \(\frac{1+2}{25} = \frac{3}{25}\)

P(2) = \(\frac{2+2}{25} = \frac{4}{25}\)

P(3) = \(\frac{3+2}{25} = \frac{5}{25}\)

P(4) = \(\frac{4+2}{25} = \frac{6}{25}\)

P(5) = \(\frac{5+2}{25} = \frac{7}{25}\)

Now, by the definition of discrete probability distribution, we must have

(1) p(x) > 0 and (2) Σp(x) = 1.

Now, p(x_i) > 0 for (i = 1, 2, 3, 4, 5) and

Σp(x_i) = p(1) + p(2) + p(3) + p(4) + p(5)

= \(\frac{3}{25}+\frac{4}{25}+\frac{5}{25}+\frac{6}{25}+\frac{7}{25} \)= 1

Thus, conditions of probability distribution of discrete random variable are satisfied. So the given distribution is a probability distribution of a discrete random variable X.