UPCET / UPSEE Parameter Recovery — practice questions

Explore 2 free Parameter Recovery questions in UPCET / UPSEE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Parameter Recovery questions and exercises with answers

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If $E(X) = 6$ and $\text{Var}(X) = 4.2$ for $X \sim B(n, p)$, then $n$ and $p$ are:Read the answer and worked solution →Mean and variance of a binomial distribution are 18 and 12 respectively. The value of $n$ is:Read the answer and worked solution →

Worked practice questions

If $E(X) = 6$ and $\text{Var}(X) = 4.2$ for $X \sim B(n, p)$, then $n$ and $p$ are:

$n = 20, p = 0.3$
$n = 10, p = 0.6$
$n = 30, p = 0.2$
$n = 12, p = 0.5$

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Correct answer: A. $n = 20, p = 0.3$

$q = \text{Var}/E = 4.2/6 = 0.7$ ⇒ $p = 0.3$. Then $np = 6$ ⇒ $n = 6/0.3 = 20$.

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Mean and variance of a binomial distribution are 18 and 12 respectively. The value of $n$ is:

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Correct answer: C. 54

$np = 18, npq = 12$ ⇒ $q = 12/18 = 2/3, p = 1/3$. $n = np/p = 18/(1/3) = 54$.