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 &#8230; . . . } and P ( X = x ) = c x x ! , for x = 1 , 2 , 3 , &#8230; &#8230; Then the value of C is

Aicharya · Accepted Answer

Given: P X = x = c x x ! &#8757; &#160; &#8721; P X = 1 &#8658; &#160; c + c 2 2 ! + c 3 3 ! + . . . . . = 1 &#8658; &#160; 1 + c + c 2 2 ! + c 3 3 ! + . . . . . . &#160; = 2 &#8658; &#160; e c = 2 &#8658; &#160; c log e e = log e 2 &#8658; c = ln 2

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

Solution

The range of a random variable X is { 1 , 2 , 3 &#8230; . . . } and P ( X = x ) = c x x ! , for x = 1 , 2 ,…

Solution

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