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For what value of k, f(x)=k( n!/(n-x)!x! p^x q^n-x) NOTE-HERE ^ symbol indicates power of p...

For what value of k, f(x)=k( n!/(n-x)!x! p^x q^n-x)
NOTE-HERE ^ symbol indicates power of p which is x.

Math   Statistics-And-Probability   
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Answer #1

k = 1

EXPLANATION:
Given:

,

                                 for x = 0,1,2,...n.

The value of k is got by noting that the Total Probability = 1

So, we get:

i.e.,

Applying Binomial Theorem on LHS, we get:

             (1)

Since

q + p = 1,

equation (1) becomes:

k = 1

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