Math & Statistics¶

Key Topics for DS/ML Interviews¶

Probability¶

Bayes' theorem
Conditional probability
Expected value
Variance, standard deviation

Statistics¶

Mean, median, mode
Percentiles, quartiles
Hypothesis testing (p-value, significance)
A/B testing

Linear Algebra¶

Matrix operations
Eigenvalues, eigenvectors
Dot product, cosine similarity

Common Coding Patterns¶

1. Math Properties¶

GCD/LCM
Prime numbers
Modular arithmetic

2. Bit Manipulation¶

AND, OR, XOR
Bit shifting
Count set bits

3. Combinatorics¶

Permutations, combinations
Pascal's triangle

Problems¶

Math¶

Problem	Difficulty	Link	Status
Fizz Buzz	Easy
Power of Two	Easy
Count Primes	Medium
Pow(x, n)	Medium

Bit Manipulation¶

Problem	Difficulty	Link	Status
Single Number	Easy
Number of 1 Bits	Easy
Reverse Bits	Easy

Probability/Statistics¶

Problem	Difficulty	Link	Status
Random Pick with Weight	Medium
Shuffle an Array	Medium

Common Techniques¶

# GCD
def gcd(a, b):
    while b:
        a, b = b, a % b
    return a

# LCM
def lcm(a, b):
    return a * b // gcd(a, b)

# Check if power of 2
def is_power_of_two(n):
    return n > 0 and (n & (n - 1)) == 0

# Count set bits
def count_bits(n):
    count = 0
    while n:
        count += n & 1
        n >>= 1
    return count
# Or: bin(n).count('1')

# Fast exponentiation
def power(x, n):
    if n < 0:
        x, n = 1/x, -n
    result = 1
    while n:
        if n & 1:
            result *= x
        x *= x
        n >>= 1
    return result

# Sieve of Eratosthenes
def count_primes(n):
    if n < 2:
        return 0
    is_prime = [True] * n
    is_prime[0] = is_prime[1] = False
    for i in range(2, int(n**0.5) + 1):
        if is_prime[i]:
            for j in range(i*i, n, i):
                is_prime[j] = False
    return sum(is_prime)

Interview Questions (Conceptual)¶

Probability¶

What's the probability of getting at least one 6 in 4 dice rolls?
Explain Bayes' theorem with an example
How would you simulate a fair coin with a biased one?

Statistics¶

Difference between Type I and Type II errors?
When would you use median over mean?
How do you calculate sample size for A/B test?