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Probability question

2021 · 25 Jul · Shift 2 · Q38
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  5. /2021 · 25 Jul · Shift 2 · Q38

Probability question

2021 · 25 Jul · Shift 2 · Q38

JEE MainMathematicsProbabilityMCQ+4 / −1
Let X be a random variable such that the probability function of a distribution is given by P(X=0)=12,P(X=j)=13j(j=1,2,3,...,∞)P(X = 0) = {1 \over 2},P(X = j) = {1 \over {{3^j}}}(j = 1,2,3,...,\infty )P(X=0)=21​,P(X=j)=3j1​(j=1,2,3,...,∞). Then the mean of the distribution and P(X is positive and even) respectively are :
  1. A
    38{3 \over 8}83​ and 18{1 \over 8}81​
  2. B
    34{3 \over 4}43​ and 18{1 \over 8}81​
  3. C
    34{3 \over 4}43​ and 19{1 \over 9}91​
  4. D
    34{3 \over 4}43​ and 116{1 \over 16}161​
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