If the probability that the random variable takes the value is given by

where is a constant, th…

Question

If the probability that the random variable  takes the value  is given by

where  is a constant, then  is equal to

CGP EDU Academic Team · Accepted Answer

The correct answer is A. To find  , we first determine the constant  using the total probability for  .
The probability  is given by:

The total probability must equal 1:

Calculating that series:

Therefore, dividing the series by 3:

Subtracting these:

The resulting series is a geometric series:

The sum of the infinite geometric series is:

Equating:

Thus, solving for  :

Next, compute  :

Calculating these:

Adding these probabilities:

Finally, calculate  :

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