QJEEM21Ma4a78: JEE Main 2021 Mathematics - Class 12 JEEM21Ma4a78 Solution: Let X be a random variable such that the probability function…

Question

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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, . . ., \infty)

. Then the mean of the distribution and P(X is positive and even) respectively are :

Accepted Answer

Mean =

\sum X_{i} P_{i} = \sum_{r = 0}^{\infty} r . \frac{1}{3^{r}} = \frac{3}{4}

P(X is even)

= \frac{1}{3^{2}} + \frac{1}{3^{4}} + . . . \infty

= \frac{\frac{1}{9}}{1 - \frac{1}{9}} = \frac{1 / 9}{8 / 9} = \frac{1}{8}

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