#!/usr/bin/env python
# coding: utf-8

# # [Homework Week 9](https://tsoo-math.github.io/ucl/QHW4.html)
# 
# For complete written solutions, please [see](https://tsoo-math.github.io/ucl/QHW4-sol.html).  We will mainly be concerned with the Python code here.

# ## Random deletion

# In[1]:


import numpy as np

number=10000
inter = np.random.exponential(1/2,number)   #notice it is parametrized by scale rather than rate
arr = np.cumsum(inter)
L = len(arr)
coin = np.random.binomial(1,0.5, L)
coinindex=-99
for i in range(L):
    if coin[i]==0:
        coinindex = np.append(coinindex, i)
coinindex = np.delete(coinindex, 0)

arrthin = np.delete(arr,coinindex)
interthin = arrthin[0]
for i in range(len(arrthin)-1):
    interthin = np.append(interthin, arrthin[i+1] - arrthin[i])

    
import matplotlib.pyplot as plt

z=interthin
    
plt.hist(z, bins = 50, density=True, label='Proability Histogram') 
t=np.linspace(0,5,num=2000)
plt.plot(t,1*np.exp(-1*t), label='Exact Density')
plt.legend(loc='upper left')
plt.show()
                          
                          


# ## Poisson process on a disc

# In[2]:


def point():
    x=1
    y=1
    while(x**2 + y**2 >=1):
        x= 2*np.random.uniform() -1
        y= 2*np.random.uniform() -1
    return np.array([x,y])

pois = [point() for _ in range(np.random.poisson(100*np.math.pi)  )  ]

L= len(pois)
x=100
y=100
for i in range(L):
    x = np.append(x, pois[i][0])
    y = np.append(y, pois[i][1])

x = np.delete(x, 0)
y = np.delete(y, 0)


import matplotlib.pyplot as plt

t=np.linspace(-1,1,num=500)


plt.figure(figsize = (10,10))
plt.plot(x,y, 'r*')
plt.plot(t, np.sqrt(1-t**2))
plt.plot(t, -np.sqrt(1-t**2))
plt.title("Poisson process on a disc", fontsize=10)



plt.show()


    



# ## Endnotes
# 
# Use the ipynb [source](https://tsoo-math.github.io/ucl2/2021-hw-week9.ipynb) for the most update version.

# In[3]:


from datetime import datetime
print(datetime.now())


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