Statement of Completion#1c583313
Juanjo Carrasco has successfully completed this project.
Basic concepts of Probability
medium
Discrete uniform
Resolution
Activities
Section 1¶
In [1]:
import pandas as pd
import numpy as np
from scipy.stats import randint
Activity 1: A telephone number is selected at random from a directory. Suppose $X$ denote the last digit of selected telephone number. Find the probability that the last digit of the selected number is 6¶
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Activity 2. A telephone number is selected at random from a directory. Suppose $X$ denote the last digit of selected telephone number. Find the probability that the last digit of the selected number is less than 3¶
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Activity 3. A telephone number is selected at random from a directory. Suppose $X$ denote the last digit of selected telephone number. Find the probability that the last digit of the selected number is greater than or equal to 8¶
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Activity 4. Let $X$ denote the number appear on the top of a die. Then $X$ the random variable take the values {1,2,3,4,5,6} and $X$ follows the uniform distribution.¶
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Activity 5. If $X$ is uniformly distributed over (0, 10), calculate the probability that $P(3 < X < 8$)¶
In [2]:
4/10
Out[2]:
0.4
Activity 6. If $Y$ is uniformly distributed over (0, 20), calculate the probability that $P(5 < Y < 15)$¶
In [3]:
# Calculate the width of the interval
interval_width = 15 - 5
# Calculate the total width of the distribution
total_width = 20
# Calculate the probability
probability = interval_width / total_width
print("Probability P(5 < X < 15):", probability)
Probability P(5 < X < 15): 0.5
Activity 7. Let the random variable $X$ have a discrete uniform distribution on the intehers $1 \leq x \leq 3$. Determine the mean and variance of $X$.¶
In [4]:
(3+1) / 2
Out[4]:
2.0
In [6]:
((3-1+1)**2 -1) / 12
Out[6]:
0.6666666666666666
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