Combinations / Permutations
If you flip a fair coin two times, what is the probability of getting exactly one head?
1/2
What is the distribution used to calculate probabilities for several independent events, all with identical probabilities of one of two possible outcomes?
Binomial
This theorem finds the limit of a function by "squeezing" it between two other functions
Squeeze Theorem
C++: what must replace the ??? to print "SASSA" ?
#include <iostream>
int main()
{
??? << "SASSA";
return 0;
}
std::cout
Combination vs Permutation: Which one of the following is used to describe counting events when order matters?
Permutation
Imagine a class of 100 students takes a test where the scores follow the Normal Distribution. with a mean of 75 and a standard deviation of 5.
How many students scored above 75?
50
Find the limit as n goes to infinity of 𝑔(𝑛) = 𝑛²/𝑒ⁿ
𝑔(𝑛) goes to 0
Python: What is printed?
import statistics
data = [1, 1, 2, 3, 6]
print(statistics.median(data))
2
12 students are enrolled in Calculus. 10 students are enrolled in statistics. 5 students are enrolled in both.
How many students are enrolled in at least one of these two courses?
17
An insurance company approves 80% of life insurance applications. If the company reviews 10 applications, what is the expected number of approved applications?
8
Find the indefinite integral of 𝑥 + 𝑐𝑜𝑠(𝑥) .
𝑥²/2 - 𝑐𝑜𝑠(𝑥) + 𝐶
R: What function is used to change EXISTING levels into factors? (Multiple answers can be correct)
as.factor()
(or stringsAsFactors = TRUE when reading in the file)
You have a bookshelf with 4 unique textbooks. How many ways can you arrange all 4 books on the shelf? (Answer can be left in factorial form)
4! = 24
A claims processing center receives, on average, 3 calls per hour. The arrivals follow a Poisson distribution.
What is the probability that the center receives at least 2 calls in a specific hour?
0.8 or 80%
Find the gradient vector of f(x, y) = 3x2 + 5y3 - 7
f(x, y) = (6x, 15y2)
Which of the following is the correct order of clauses in a standard SQL query?
a) SELECT, FROM, WHERE, GROUP BY, HAVING
b) FROM, SELECT, WHERE, GROUP BY, HAVING
c) SELECT, WHERE, FROM, HAVING, GROUP BY
d) FROM, WHERE, SELECT, GROUP BY, HAVING
a) SELECT, FROM, WHERE, GROUP BY, HAVING