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  • Try this! If X has a binomial distribution, B(n, p) with parameters n and p such that P(X=2)=P(X=3), then E(X), the mean of variable X, is :

If X has a binomial distribution, B(n, p) with parameters n and p such that P(X=2)=P(X=3), then E(X), the mean of variable X, is :

  • Option 1)

    2-p

  • Option 2)

    3-p

  • Option 3)

    \frac{p}{2}

  • Option 4)

    \frac{p}{3}

 

Answers (1)

best_answer

As we have learned

Binomial Distribution -

In a series of n independent trials if the probability of success P in each trial is same, then the probapility of r success is

P(X=r)= \left\{\begin{matrix} \left ( \frac{n}{r} \right )\: q^{n-r}\cdot P^{r} & q = 1-P\\ \left ( \frac{n}{r} \right )\frac{1}{2^{n}} &P=\frac{1}{2} \end{matrix}\right.

- wherein

Where \sum is probability of failure.

 

 

Binomial Distribution(Statistical) -

Mean = np

Variance = npq

Standard \: deviation =\sqrt{npq}

-

 

 P (x= 2 )= ^2 C_2 P^2 (1-P )^{n-2}

P (x= 3 )= ^2 C_3 P^3 (1-P )^{n-3}

 

So , = ^n C_2 P^2 (1-P )^{n-2}= ^nC_3 P^3 (1-P )^{n-3}

\Rightarrow 3(1-P )= nP-2P \\ \Rightarrow 3 = nP+P\\ \Rightarrow P =\frac{3}{n+1}\Rightarrow n = \frac{3- P}{P}

Now E(x ) = nP = \left ( \frac{3-p}{p} \right )p= (3-p)

 

 

 

 


Option 1)

2-p

Option 2)

3-p

Option 3)

\frac{p}{2}

Option 4)

\frac{p}{3}

Posted by

gaurav

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