Let X be a discrete random variable whose probability distribution is defined as follows: where k is a constant. Calculate (i) the value of k (ii) E (X) (iii) Standard deviation of X.

(i) Given,

   

for

   

So,

   

   

   

   

Also,

   

for

   

   

   

   

And, for otherwise it is

   

.

Thus, the probability distribution is given by

We know that,

   

So,

   

⇒

   

   

Therefore, the value of k is

   

.

(ii) Now, the probability distribution is

   

=

   

=

   

=

   

(ii) We know that the standard deviation (SD) = √Variance

Variance =