Question

A random variable $X$ has the following probability distribution:

X	0	1	2	3	4	5	6	7
P(X)	0	m	2m	2m	3m	m²	2m²	7m² + m

The value of m is:

• A. 10
• B. $\frac{1}{10}$
• C. -1 and $\frac{1}{10}$
• D. $\frac{1}{20}$

Answer 1

Answer: (B)

$\frac{1}{10}$

Answer 2

The sum of probabilities in a probability distribution must equal 1:

$\sum P(X) = 1$.

Substitute the given probabilities:

0m + 2m + 2m + 3m + 3m + $2m^2 + 2m^2 + (7m^2 + m)$ = 1.

Simplify:

$12m + 11m^2 = 1$.

Factorize:

$m(12 + 11m) = 1$.

$m = \frac{1}{10}$ (since $m > 0$).

Thus, $m = \frac{1}{10}$.