Homework 2
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
Homework 2
Due date: Feb. 03.
❼ Question 1a: In the class Normal distribution N[µ,σ2 ] was discussed.
− (x − µ)2
Using the PDF of the Normal distribution, fX (x) = e 2 σ 2 , plot the bell curves for the following parameters. [Points 15]
– µ = 0,σ2 = 1. Let RV X ϵ[−8, 8].
– µ = −5,σ2 = 6. Let RV X ϵ[−15, 15].
– µ = 100,σ2 = 0.5. Let RV X ϵ[−105, 105]. Submit appropriately labeled visuals.
❼ Question 1b: In the class Poisson Distribution P[λ] was discussed. Using
the Probability Mass Function (PMF) of the Poisson distribution, P[X =
i] = e −λ , where λ, plot the PMF for the following parameters. [Points
15]
– λ = 0.03.
– λ = 50.
– λ = 1000.
Choose appropriate ranges of RV X for each parameter value. Submit appropriately labeled visuals.
❼ Question 2: [Points 20]
Part a: Simulate the Poisson random process Xt for t ϵ0, . . . , 100. Let λ = 50. Repeat the simulation four times.
Part b: Simulate the Normal random process Xt for t ϵ0, . . . , 100. Let µ = 0,σ2 = 1. Repeat the simulation four times.
Submit appropriately labeled visuals.
❼ Example code HW2 ExampleCode.py is posted.
❼ Question 3: [Points 20]
Part a: Run the example code HW2 ExampleCode 2.py for plotting autocorrelation and PSD for “IPN31152N Fred Industrial Production Manufacturing Non-Durable Goods Ice Cream and Frozen Dessert.xlsx” .
Part b: Run the example code HW2 ExampleCode 2.py for plotting autocorrelation and PSD for “WholeFood.xlsx”, “Pharmaceutical.xlsx”, and “Viscosity.xlsx” . And provide a 50-word description of each.
Submit appropriately labeled visuals.
❼ Example code HW2 ExampleCode 2.py is posted.
❼ Data sets “IPN31152N Fred Industrial Production Manufacturing Non-
Durable Goods Ice Cream and Frozen Dessert.xlsx”, “WholeFood.xlsx”, “Pharmaceutical.xlsx”, and “Viscosity.xlsx” are posted.
2023-02-01