Page 206 - DMTH404_STATISTICS

Statistics

Notes 14.9 Self Assessment

1. ................... is a theoretical probability distribution which was given by James Bernoulli.
(a) expected (b) Binomial distribution
(c) probability mass function (d) discrete values

2. The fitting of a distribution to given data implies the determination of ...................
(or theoretical) frequencies for different values of the random variable on the basis of this
data.
(a) expected (b) Binomial distribution
(c) probability mass function (d) discrete values
3. A discrete random variable is said to follow a uniform distribution if it takes various
................... with equal probabilities.
(a) expected (b) Binomial distribution
(c) probability mass function (d) discrete values

4. Poisson distribution was derived by a noted mathematician, Simon D. Poisson, in ...................
(a) expected (b) 1837
(c) probability mass function (d) discrete values
5. The ................... (p.m.f.) of Poisson distribution can be derived as a limit of p.m.f. of binomial
distribution when n   such that m (= np) remains constant.
(a) expected (b) Binomial distribution
(c) probability mass function (d) discrete values

14.10 Review Questions

1
1. (a) The probability of a man hitting a target is . (i) If he fires 7 times, what is the
4
probability of his hitting the target at least twice? (ii) How many times must he fire
2
so that the probability of his hitting the target at least once is greater than ?
3
(b) How many dice must be thrown so that there is better than even chance of obtaining
at least one six?
3 F I n
Hint : (a)(ii) Probability of hitting the target at least once in n trials is 1- 4 H K . Find n
5 F I n
2 1
such that this value is greater than . (b) Find n so that 1- 6 H K > .
3 2
2. A machine produces an average of 20% defective bolts. A batch is accepted if a sample of
5 bolts taken from the batch contains no defective and rejected if the sample contains 3 or
more defectives. In other cases, a second sample is taken. What is the probability that the
second sample is required?
Hint : A second sample is required if the first sample is neither rejected nor accepted.

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