Part CCSIR NET June 2025theta-is-at-most-the-minimum-so-the-interval-cannot-reach-above-y

Theta is at most the minimum so the interval cannot reach above y

Let $X_{1}, X_{2}, \dots, X_{n}$ be independent and identically distributed random variables with the probability density function f(x| $θ) =$ $e^{- (x - θ)}$ if $x \geq θ$ , and 0 otherwise, where $θ \in R$ is the unknown parameter. Further, let $Y = min (X_{1}, X_{2}, \dots, X_{n})$ . Which of the following are confidence intervals for $θ$ with the confidence coefficient $(1 - α)$ , where $α \in (0, 1)$ ?

A. $(Y + (1/ n) ln (1 - α /2), Y - (1/ n) ln (1 - α /2))$
B. $(Y + (1/2 n) ln (α), Y)$
C. $(Y + (2/ n) ln (α /2), Y + (2/ n) ln (1 - α /2))$ ✓
D. $(Y + (1/ n) ln (α /2), Y + (1/ n) ln (1 - α /2))$ ✓

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests boundary and endpoint.

See pricing

50 are analysed free — try those first.

The trap it tests

Boundary and endpoint

The statement turns at the edge of the interval, the domain, or the parameter range.

Drill statements like this

Theta is at most the minimum so the interval cannot reach above y

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