The range of a random variable X is { 1 , 2 , 3 … . . . } and P ( X = x ) = c x x ! , for x = 1 , 2 , 3 , … … Then the value of C is

Question

The range of a random variable X is { 1 , 2 , 3 … . . . } and P ( X = x ) = c x x ! , for x = 1 , 2 , 3 , … … Then the value of C is, 0, 1, ln ( 2 ) ( where ln denotes the natural log ), ln ( 3 ) ( where ln denotes the natural log )

MARKS App · Accepted Answer

Given: P X = x = c x x ! ∵ ∑ P X = 1 ⇒ c + c 2 2 ! + c 3 3 ! + . . . . . = 1 ⇒ 1 + c + c 2 2 ! + c 3 3 ! + . . . . . . = 2 ⇒ e c = 2 ⇒ c log e e = log e 2 ⇒ c = ln 2

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