Question

please answer step by step​

Answer 1

Answer:

(B) $\frac{294}{251\\}$  

Step-by-step explanation:

$P(x)=\frac{c}{x^{3} } ; x = 1,2,3$

       $= 0$       otherwise

$P(1)+P(2)+P(3)=1$

$\frac{C}{1^{3} } +\frac{C}{2^{3} } +\frac{C}{3^{3} } =1\\\\C\times(\frac{1}{1^{3} } +\frac{1}{2^{3} } +\frac{1}{3^{3} } )=1$

$C\times(1+\frac{1}{8} +\frac{1}{27} )=1\\\\C\times(\frac{8\times27+8+27}{8\times27} )=1$

$C\times(\frac{251}{8\times27} )=1$

$C=\frac{8\times27}{251}$

$E(x)=?$

E(x) = ∑ [ xi × P(xi) ]

$x=1,2,3$

$E(x)=1\times P(1)+2\times P(2)+3\times P(3)$

       $=1\times \frac{C}{1^{3} } +2\times \frac{C}{2^{3} } +3\times \frac{C}{3^{3} }$

$C\times (\frac{1}{1^{3} } +\frac{2}{2^{3} } +\frac{3}{3^{3} } ) = C\times(\frac{1}{1^{2} } +\frac{1}{2^{2} } +\frac{1}{3^{2} } )$

$=\frac{8\times27}{251} \times (1+\frac{1}{4} +\frac{1}{9} )$

$= (\frac{294}{251} )$