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If a random variable X has the p.d.f. f(...

If a random variable X has the p.d.f. `f(x)=k/(x^(2)+1), 0 lt x lt infty`, then k is

A

`pi`

B

`1/pi`

C

1

D

`2/pi`

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The correct Answer is:
D
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SURA PUBLICATION-PROBABILITY DISTRIBUTIONS-ADDITIONAL QUESTIONS - 1 MARKS
  1. If E(x)=1/2, E(x^(2))=1/4 then var(x) is

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  2. If f(x)=Cx^(2), o lt x lt 2 is the p.d.f. of x then c is

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  3. If a random variable X has the p.d.f. f(x)=k/(x^(2)+1), 0 lt x lt inft...

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  4. In eight throws of a die, 1 or 3 is considered a success. Then the mea...

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  5. The random variable X has variance 4 and E(x^(2))=8, then the mean of ...

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  6. In a binomial distribution, if the mean is 8 and the variance is 6, th...

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  7. In a binomial distribution, n=4, P(X=0)=16/81, then P(X=4).

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  8. A die is tossed 5 times Getting an odd number is considered a success....

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  9. Var(2x pm 5) is = .

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  10. If the p.d.f. f(x)={{:(x/2",", 0 lt x lt 2), (0",", "elsewhere"):} the...

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  11. The variance of a binomial distribution is .

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  12. In a binomial distribution n=4, P(X=0)=16/81, then P(X=4) is .

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  13. A coin is tossed 3 times. The probability of getting exactly 2 heads i...

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  14. The sum of the mean and variance of a binomial distribution for 6 tota...

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  15. If the mean and variance of a binomial variate are 2 and 1 respectivel...

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  16. A die is thrown 10 times. Getting a number greater than 3 is considere...

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  17. If X is a continuous random variable then P(X ge a)= .

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  18. If X is a continuous random variable then p(a lt x lt b)= .

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  19. If X is a continuous random variable then which of the following is in...

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  20. If F(x) is a distribution function of a random variable then the false...

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