Question

For a continuous random variable y, the median is the value φ.5 such that P(y ≤ φ.5) = 0.5. What is the median of the uniform distribution on the interval (θ1, θ2)?

a) (θ₁ + θ₂)/2
b) θ₁
c) θ₂
d) (θ₁ + θ₂)/4

Answer 1

The median of the uniform distribution on the interval (θ1, θ2) is (θ1 + θ2)/2.

Step-by-step explanation:

The median of a continuous random variable y is the value φ.5 such that P(y ≤ φ.5) = 0.5. For a uniform distribution on the interval (θ1, θ2), the probability density function is constant within the interval and zero outside the interval. The probability of a value of y being less than or equal to φ.5 is 0.5.

Therefore, the median of the uniform distribution on the interval (θ1, θ2) is (θ1 + θ2)/2.