Let y 1 , y 2 , , y n be a random sample from a Poisson distribution with mean Suppose we use y as an estimator of Derive a (1 )100 confidence interval for Start with the pivotal statistic and show that for large samples, Z is approximately a standard normal random variable Then substitute y for in...

Let y y1 y2 ynn be the sample mean Since the sample i ...

Let y 1 , y 2 , . . . , y n be a random sample

Question:

Let y₁, y₂, . . . , y_n be a random sample from a Poisson distribution with mean λ. Suppose we use y̅ as an estimator of λ. Derive a (1 - α)100% confidence interval for λ. Start with the pivotal statistic

and show that for large samples, Z is approximately a standard normal random variable. Then substitute y̅ for λ in the denominator (why can you do this?) and follow the pivotal method of Example 7.6.

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