The probability that a newly designed electronic component will survive a given shock test is 5/6. Find the probability that exactly 3 of the next 4 components tested survive.
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The distribution function F of a continuous variable is given by
F(x) = 0, if x < 0
= x 2 , if 0 < x < 1
= 1, if x > 3
(i) Find the pdf of X,
(ii) Evaluate P[|X| <1/ 2], using distribution function F,
(iii) Evaluate P[|X| < 1/ 2], using pdf.
A taxi cab company has 12 Ambassadors and 8 Fiats. If 5 of these taxi cabs are in the workshop for repair and an Ambassador is as likely to be in for repair as a Fiat, what is the probability that (i) 3 of them are Ambassadors and 2 are Fiats, (ii) at least 3 of them are Ambassadors, and (iii) all 5 are of the same make?
Ms. X thinks that there is a 30% chance that her company will set up a branch office in New Delhi. If it is so, then she is 60% certain that she will be assigned the responsibilities of a branch manager there. What is the probability that Ms. X will be branch manager at the New Delhi office?
State whether the following statements are True or False and also give the reason in support of your answer.
(a) If odds in favour of an event A are 2:5 then probability of happening of the event A will be .
(b) If two independent events A and B are such that A and B are independent. P(A) = and P(B) =
, then events A and
are independent.
c) If X is a discrete random variable with probability mass function (pmf)
| X | 0 | 1 | 2 |
| P[X=x] | 1 4 | 1 2 | a |
The probability that the dial will land somewhere between 0° and 90° will be .
The joint density function of random variables X and Y is given by
Are X and Y independent?
The probability that a person living in a certain city owns a dog is estimated to be 0.3. Find the probability that the tenth person randomly interviewed in that city is the fifth one to own a dog.
A company has installed 10,000 electric lamps in a metro. If these lamps have an average life of 1,000 burning hours with a S.D. of 200 hours. Assuming normality, what number of lamps might be expected to fail.
i) in the first 800 burning hours.
ii) between 800 and 1200 burning hours.
iii) more than 1000 burning hours