Uniform Distribution

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GRE Quantitative Reasoning › Uniform Distribution

Questions 1 - 1

X is a continuously and uniformly distributed on the interval (0,50). Find the Expected Value (E\[x\]) and Variance (Var(x)) of X.

Because x is a continuous uniform random variable the expected value and variance can be found with the following formulas:

$E[x]=\frac{a+b}{2}$

$Var(x)=\frac{(b-a)^2}{12}$

X is uniform on (a,b). In this case a is 0 and b is 50. Plugging the values of a and b into the given formulas will give the answers:

$E[x]=\frac{a+b}{2}=\frac{0+50}{2}=25$

$Var(x)=\frac{(b-a)^2}{12}=\frac{2500}{12}=208.33$