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WBJEE Mean and Variance — practice questions

Explore 4 free Mean and Variance questions in WBJEE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Mean and Variance questions and exercises with answers

Showing questions 1–4 of 4.

For a Binomial distribution $X \sim B(n, p)$, the **mean** (expected value) is:Read the answer and worked solution →For a Binomial distribution $X \sim B(n, p)$, the **variance** is:Read the answer and worked solution →If $X \sim B(10, 0.4)$, then $E(X)$ and $\text{Var}(X)$ are respectively:Read the answer and worked solution →Mean and variance of a binomial distribution are 4 and 2 respectively. The probability of **exactly 2** successes is:Read the answer and worked solution →

Worked practice questions

For a Binomial distribution $X \sim B(n, p)$, the **mean** (expected value) is:

  1. $np$
  2. $npq$
  3. $\sqrt{npq}$
  4. $p/n$
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Correct answer: A. $np$

Mean $E(X) = np$. For a single Bernoulli trial $E = p$ by linearity, $n$ independent trials give $E = np$.

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For a Binomial distribution $X \sim B(n, p)$, the **variance** is:

  1. $np$
  2. $npq$ where $q = 1 - p$
  3. $\sqrt{np}$
  4. $n^2 p^2$
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Correct answer: B. $npq$ where $q = 1 - p$

Var$(X) = npq$. *Note: variance ≤ mean for binomial (since $q \le 1$), with equality only when $p = 0$.*

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If $X \sim B(10, 0.4)$, then $E(X)$ and $\text{Var}(X)$ are respectively:

  1. 4 and 2.4
  2. 4 and 4
  3. 0.4 and 0.24
  4. 10 and 4
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Correct answer: A. 4 and 2.4

$E(X) = np = 10 \times 0.4 = 4$. $\text{Var}(X) = npq = 10 \times 0.4 \times 0.6 = 2.4$.

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More Mathematics topics

SequencesProbability & StatisticsBinomial TheoremSequences and SeriesGeometryLinear ProgrammingLimits and ContinuityPermutations and Combinations