Let X be a random variable such that the probability function of a distribution is given by P X = 0 = 1 2 , P X = j = 1 3 j j = 1 , 2 , 3 , … , ∞ . Then the mean of the distribution and P ( X is positive and even ) respectively, are:

Question

Let X be a random variable such that the probability function of a distribution is given by P X = 0 = 1 2 , P X = j = 1 3 j j = 1 , 2 , 3 , &#8230; , &#8734; . Then the mean of the distribution and P ( X is positive and even ) respectively, are:

Aicharya · Accepted Answer

We have, P X = 0 = 1 2 , P X = j = 1 3 j j = 1 , 2 , 3 , &#8230; , &#8734; Mean = &#931; X i P i = &#8721; r = 0 &#8734; r &#183; 1 3 r = 3 4 P ( X is even) = 1 3 2 + 1 3 4 + &#8230; &#8734; = 1 9 1 - 1 9 = 1 9 8 9 = 1 8 .

Let X be a random variable such that the probability function of a distribution is given by P X = 0 = 1 2 ,…

Solution