Question

7. For a discrete random variable, the set of possible values is a. an interval of real numbers. b. a set of numbers that is countable. c. a set of numbers that has a finite number of numbers. d. none of the above. 8. Let X be a continuous random variable, then P( X = 0) is a. 0.00001. b. zero. c. can be large in some random variable. d. none of the above. 9. For a discrete random variable, the probability of the random variable takes a value within a very small interval must be a. zero. b. very small. c. close to 1. d. none of the above. 10. The area under the density function in a certain interval of a continuous random variable represents a. randomness. b. the area of one rectangle. c. the probability of the interval. d. none of the above. 11. For any random variable, X, E(X)= a. X. b. 0. c. some fixed number. d. None of the above. 12. If E(X) = 0, then the minimum value of X cannot be a greater than -1. b. greater than 0. c. less than-1. d. none of the above.

Answer 1

Answer 7) option b) is correct.

For a discrete variable, a set of possible values are the set of numbers that are countable like 0, 1, 2 etc.

Answer 8) option b) is correct.

If X is a continous variable the P(X= 0) is zero because at point of time the probability is zero in continous distribution.

Answer 9) option d) is correct.

The probability for a discrete variable lies between the small interval which 0 to 1.

Answer 10) option c) is correct.

The area under the density curve in continous distribution is the probabilty between the interval i.e P(a<x>b)

Answer 11) option c) is correct.

For a random variable X, E(X) is some fixed number as E(aX +b) = a+b.

Answer 12) option d) is correct.

If E(X) =0 then minimum value of X is equal to 0 because expectation of a constant is constant so there is no other number whose expection is zero.

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