Algorithms Answers

two integers and initialize them to 199 and 76. Display the sum, difference, product, average, square, and remainder of the values.

Write an algorithm that displays a series of the Celsius temperatures 0 through a termination value and their Fahrenheit equivalents. The formula for converting a temperature from Celsius to Fahrenheit equivalents. The formula for converting a temperature from Celsius to Fahrenheit is

                                      F = 9/5 C + 32

Where F is the Fahrenheit temperature and C is the Celsius temperature. Your algorithm must use a loop to display the series.

Sample Output of the program is given below.

Enter the highest Celsius temperature value: 5

Fahrenheit equivalent of 0 is 32

Fahrenheit equivalent of 1 is 33.8

Fahrenheit equivalent of 2 is 35.6

Fahrenheit equivalent of 3 is 37.4

Fahrenheit equivalent of 4 is 39.2

Fahrenheit equivalent of 5 is 41

A random variable X ~ bino(5, 0.3). g(x) is a continuous and differentiable function on the interval (0, 5).

a. Write down the cumulative distribution function F(x) for the random variable X.

b. g(x) is an approximation of F(x). Construct g(x).

Let 𝐼 = ₀∫¹⁰ 𝑓(𝑥)𝑑x . You are asked to approximate the value of I using (i) uniform random 0 10 ∫ 𝑓(𝑥)𝑑𝑥 variable, (ii) Monte Carlo simulation and (iii) antithetic variates

a. Write down the procedures for the Monte Carlo simulation without using antithetic variates.

b. Write down the antithetic variable.

X = [0.01, 0.36, 0.97, 0.44, 0.86, 0.49, 0.02, 0.19, 0.54, 0.63, 0.69, 0.27, 0.21, 0.55, 0.54, 0.1 , 0.02, 0.49 , 0.42, 0.79], is a list of 20 random numbers generated from a pseudo-random number generator G.

a. What is a uniformity test?

b. Using Chi-square Goodness-of-fit test with 4 bins, test whether X belongs to U(0, 1) based on 5% significant level. 

c. Can we conclude G generates truly random numbers following the distribution U(0, 1)?

Given a multi-linear regression model: Y = 2X₁- 3X₂ + 1.5X₃ - 0.5, and 10 data points.

Y X₁ X₂ X₃

-------------------------------------------------------------------------------------------------

5 1 0 3

3 1 1 3

5 1 1 5

-1 1 3 5

5 2 0 1

0 2 2 1

3 2 3 5

4 3 1 1

0 3 3 3

6 5 2 1

a. Which parameter is the model sensitive to?

b. Evaluate R²

c. Evaluate adjusted R²

1. The following names of students are stored in an array with the identifier studentnames. studentnames = ["Rob", "Anna", "Huw", "Emma", "Patrice", "Iqbal"] Describe the steps that a linear search would take to find Anna in studentnames

Convert -3.5 to binary notation in 8 bit floating format

Consider this data listing relationships between members on a social network:

Jessica's friend list: Meghan, Alan, Martin

Meghan's friend list: Alan, Lori

Tony’s friend list: Lori, Meghan

Martin's friend list: Lori, Meghan

Alan's friend list: Martin, Jessica

Lori's friend list: Meghan

Consider how we can use graph techniques to express the various relationships between these members.

14. Construct a directed adjacency matrix to represent this data.

15. Compute the in/out degree of each vertex.

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Write an algorithm that displays an equivalent color once an input letter matches its first character.