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SEMESTER - I
MID SEMESTER EXAMINATION
ELEMENTS OF STATISTICS
MCQS = UNIT - 4
1. If the probability of male birth is 0·5, then the probability that in a family of 4 children there will be at least 1 boy, is
a) 4/16
b) 12/16
c) 11/16
d) 15/16
2. If the mean and variance of a binomial distribution with parameters (n, p) are 40 and 30 respectively, then parameters are :
a) (40, 0·75)
b) (30, 0·25)
c) (160, 0·25)
d) (120, 0·5)
3. If a random variate X follows binomial distribution with the values of the parameters as 9 and p, then maximum value of the variance of X is
a) 2
b) 2·25
c) 4·5
d) 4.
4. If the probability of a defective bolt is 1/10, find (i) the mean; (ii) Variable; for the distribution of defective bolts in a total of 20.
Ans : (2, 1.8)
5. If X be a Poisson random variable such that P(X = 0) = P(X = 1), then E(X) is
a) e
b) 1
c) 1/e
d) 0.5
6. If a random variable X follows Poisson distribution such that P(X = 1) = P(X = 2), find the mean and variance of the distribution.
Ans. Mean = Variance = 2.
7. In a Binomial Distribution, if ‘n’ is the number of trials and ‘p’ is the probability of success, then the mean value is given by ___________
a) np
b) n
c) p
d) np(1-p)
8. In Binomial Distribution
a) Mean = Variance
b) Mean > Variance
c) Mean < Variance
d) Mean = Standard Deviation
9. In Poisson distribution
a) Mean = Variance
b) Mean > Variance
c) Mean < Variance
d) Mean = Standard Deviation
10. Which of the following statement is not true for Binomial distribution?
a) The random experiment is performed repeatedly a finite number of times
b) The outcomes of the random experiment (trial) results in the dichotomous classification of events.
c) All the trails are dependent.
d) The probability of success in any trail is p and is constant for each trail.
11. Poisson distribution is limiting case of Binomial distribution if
a) The random experiment is performed repeatedly a finite number of times
b) The random experiment is performed repeatedly large number of times and probability of success in each trial is small
c) The random experiment is performed repeatedly finite number of times and probability of success in each trial is
small
d) The random experiment is performed repeatedly finite number of times and probability of success in each trial is
always 0.5
12. Which of the following is Binomial Variate?
a) Number of train arrive at platform during a day
b) Number of defective items in a lot of 10
c) Number of printing mistake per page
d) Number of death during a year due to rare dieses.
13. If probability of success in each trial is more than failure then Binomial Distribution is
a) Symmetric
b) Positively skewed
c) Negatively skewed
d) Information are insufficient
14. If probability of success in each trial is less than failure then Binomial Distribution is
a) Symmetric
b) Positively skewed
c) Negatively skewed
d) Information are insufficient
15. If probability of success in each trial is equal to failure then Binomial Distribution is
a) Symmetric
b) Positively skewed
c) Negatively skewed
d) Information are insufficient
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