Math Problem Statement

X be a random variable which follow binomial distribution with parameters n & p. Derive the expressions for E[X] and Var[X] without using moment generating function

Solution

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Math Problem Analysis

Mathematical Concepts

Binomial Distribution
Expected Value
Variance
Linearity of Expectation
Bernoulli Trials

Formulas

E[X] = np
Var(X) = np(1 - p)
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

Theorems

Linearity of Expectation
Binomial Theorem

Suitable Grade Level

Undergraduate level (College-level probability and statistics)