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If a random variable X takes the value x...

If a random variable X takes the value `x_(k) = ((-1)^(k)2^(k))/(k) (k = 1, 2, 3,….)` with probability `P(X = x_(k)) = 2^(-k)`. Show that mean is `- log_(e) 2`.

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AAKASH SERIES-RANDOM VARIABLES-Exercise 4.1
  1. is the probability distribution of random varibale X. Find k and varia...

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  2. Find the mean and variance of the random variable X which follows the ...

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  3. The probability distribution of a random variable X is given below. ...

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  4. The range of a random variable X is {0, 1, 2}. Given that P(X=0)=3c^(3...

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  5. Let X be a random varibale such that P(X = -2) = P(X = -1) = P(X = 2...

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  6. If X is a random varibale with the following distribution where p...

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  7. The range of a random variable X = {1, 2, 3,….} and probabilities are ...

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  8. The range of a random variable X = {1, 2, 3,…} and the probability dis...

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  9. If a random variable X takes the value x(k) = ((-1)^(k)2^(k))/(k) (k =...

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  10. Two dice are rolled and the probability distribution of the sum of the...

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  11. Four bad apples are mixed with 20 good apples. If 2 apples are drawn a...

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  12. A box contain 6 tickets. Two of the tickets carry a price of Rs 5/- ea...

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  13. A buisness man gets a profit of Rs. 2800 with probability 0.5, loss of...

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  14. Two cards are drawn form pack of 52 cards one after another with repla...

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  15. Two cards are drawn from pack of 52 cards one after another without re...

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  16. A pair of fair dice is rolled 2 times. Find the mean of the number of ...

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  17. A coin is loaded such that P(H)=3P(T). It is tossed 3 times. Let X be ...

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  18. Two coins whose faces are mared 1 and 2 are tossed. Let X be the total...

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