Let X be a random variable such that the... | Probability

JEE MAIN 2021

25-07-2021 S2

Question

Let $x$ be a random variable such that the probability function of a distribution is given by $P(X=0)=\frac{1}{2}, P(X=j) =\frac{1}{3^j}(j=1,2,3, \ldots, \infty)$. Then the mean of the distribution and $\mathrm{P}(\mathrm{X}$ is positive and even) respectively are:

Select the correct option:

$\frac{3}{8}$ and $\frac{1}{8}$

$\frac{3}{4}$ and $\frac{1}{8}$

$\frac{3}{4}$ and $\frac{1}{9}$

$\frac{3}{4}$ and $\frac{1}{16}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution