show that Chebyshev’s inequality holds for a Normal distribution. Show this for µ ± 2σ and µ ± 3σ.

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STATA-Assignment

1. Show that Chebyshev’s inequality holds for a Normal distribution.

Show this for µ ± 2σ and µ ± 3σ.

Specifications: Create a dataset of 1000 observations. This dataset should have a random variable that follows a normal distribution with mean 25 and standard deviation 5.

Hints: a) Use summary command in STATA, b) create Maximum and Minimum cut-off values

for defining “Zone 2”      [10]

2. Show that Chebyshev’s inequality holds for a Poisson distribution.

Show this for µ ± 2σ.

Specifications: Create a dataset of 1000 observations. This dataset should have a random variable which follows a poisson distribution with λ = 25.

Hints: a) Use summary command in STATA, b) create Maximum and Minimum cut-off values

for defining “Zone 2”      [5]

3. Show that Central Limit holds for Poisson distribution.

Specifications: Create a dataset of 1000 observations. This dataset should have a random variable which follows a poisson distribution with λ = 25. The sample size (n) should be 30. Create a histogram to visualize the output.      [5]

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