Question

Let X be a binomial random variable, that is, X ? Bin(n, p), where n ? ? ? {0, p ? (0, 1). Using only the definition of the expectation, show that E(X) = np. Hint

Name: Let X be a binomial random variable, that is, X ? Bin(n, p), where n ? ? ? 0, p ? (0, 1). Using only the definition of the expectation, show that E(X) = np. Hint
Uploaded: 2023-04-18T02:49:57-08:00
Duration: 4 min 43 s
Channel: Madhur L
Description: Let X be a binomial random variable, that is, X ? Bin(n, p), where n ? ? ? 0, p ? (0, 1). Using only the definition of the expectation, show that E(X) = np. Hint

          Let X be a binomial random variable, that is, X ? Bin(n, p), where n ? ? ? {0, p ? (0, 1). Using only the definition of the expectation, show that E(X) = np. Hint

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

04/18/2023

Step 1

For a discrete random variable \(X\) with possible values \(x_1, x_2, \ldots\) and corresponding probabilities \(P(X = x_1), P(X = x_2), \ldots\), the expectation \(E(X)\) is given by: \[ E(X) = \sum_{i} x_i P(X = x_i) \] Show more…

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Let X be a binomial random variable, that is, X ~ Bin(n, p), where n ∈ ℕ ∪ {0, p ∈ (0, 1). Using only the definition of the expectation, show that E(X) = np. Hint