# I need math help in calculating the variance, to find variance when given range and mean [closed]

x is a random variable with range (2,3), mean=9/4 what is the variance? I need to know if what the variance is by only having the mean and range. Please help

• which is the distribution of $x$? Commented Jan 19, 2021 at 22:58
• These are the only details, the question goes as follows: x is a random variable with range consisting of {2,3}, mean=9/4. Find the variance. Commented Jan 19, 2021 at 23:02
• yes, i think so Commented Jan 19, 2021 at 23:16
• @integratethis a continuous uniform distribution has mean in the center, which would be 5/2 (fixed typo.. point was its not 9/4), so there seems to be a problem here.
– Mark
Commented Jan 19, 2021 at 23:24
• @Mark you are right. I guess op meant the probabilities are not known for the two values, but you are given $X = \{2, 3\}$ , not a "range", and the mean is $9/4$. Commented Jan 20, 2021 at 0:27

You know $$1 = p_2 + p_3$$ and $$9/4 = 2 p_2 + 3 p_3$$, so you can figure out that $$p_2 = 3/4$$. Then it's a matter of computing the variance as $$(2 - 9/4)^2p_2 + (3 - 9/4)^2p_3$$.
• The answer is $3/16$. Commented Jan 19, 2021 at 23:40
• $(-1/4)^2(3/4) + (3/4)^2(1/4) ...$ Commented Jan 19, 2021 at 23:51