Question

The range of a random variable X is $1,2,3,4,..$ and the probabilities are $P(X=K)=\frac{3^{CK}}{\angle K};$
$K=1,2,3,4$,......,then the value of C is

• A. $lo{g}_{e}3$
• B. $lo{g}_{e}2$
• C. $lo{g}_3\left(lo{g}_{e}2\right)$
• D. $lo{g}_2\left(lo{g}_{e}3\right)$

Answer 1

Answer: (C)

$lo{g}_3\left(lo{g}_{e}2\right)$

we know $e^x={\sum }_0^{\infty }{x}^k/k!and\sum P\left(i\right)=1e^{3^C}=e^0/0!+{\sum }_1^{\infty }P(x=k)=1+1=23^C{\log }_{2}e={\log }_{2}2=1C={\log }_3{\log }_{e}2$