Tag: random variables and probability distribution

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Questions Related to random variables and probability distribution

Multiple choice business maths random variables and probability distribution poisson distribution poisson distrubution probability distributions

If ${ \mu  } _{ 2 }=20,{ \mu  } _{ 2 }^{ 1 }=276$ for a discrete random variable $X$, then the mean of the random variable $X$ is

  1. $16$
  2. $5$
  3. $2$
  4. $1$
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A Correct answer
Explanation

$\mu _2=E(X^2)-[E(X)]^2......(i)$

$\mu _2'=E(X)^2.....(ii)$
Given: $\mu _2=20, \mu _2'=276$
from equation (ii) $\implies E(x^2)=276$
and from equation (i), $\implies 20=276-[E(X)]^2$
$\implies [E(X)]^2=276-20=250\\implies E(X)=16$
is the mean of random variable.