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1. Let X1,..., Xn be a random sample from an N(μ, σ2).

(a) Construct a (1 - α)100% con?dence interval for μ when the value of σ2 is known.

(b) Construct a (1 - α)100% con?dence interval for μ when the value of σ2 is unknown.

2. Let X1,..., Xn be a random sample from an N(μ1, σ2) population and Y1,..., Yn be an independent random sample from an N(μ2, σ2) distribution where σ2 is assumed to be known. Construct a (1 - α)100% interval for (μ1 - μ2). Interpret its meaning.

3. Let X1,..., Xn be a random sample from a uniform distribution on [θ, θ + 1]. Find a 99% con?dence interval for θ, using an appropriate pivot.

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