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 |
then value of a will be 1.
(d) An oil company conducts a geological study that indicates an exploratory oil well should have a 20% chance of striking oil. To find the probability that the third strike comes on the seventh well drilled, we use geometric distribution?
(e) Suppose that you spin the dial shown in the figure so that it comes to rest at a random position.
The probability that the dial will land somewhere between 0° and 90° will be .
(a) True, Because odds in favor are 2:5, this means the event can occur in 2 ways and there are 5 ways the event cannot occur this means there are 7 total outcomes and 2 are favorable the probability that the event will occur is 2/7.
(b)
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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.
The metro trains on a certain section run every 10 minutes between 5 a.m. to 10 p.m. What is the probability that a commuter entering the station at a random time during this period will have to wait
(i) at least five minutes?
(ii) zero minute?
(iii) 2 to 5 minutes?
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 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.
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?
Three technicians X, Y and Z service respectively 20%, 30% and 50% breakdowns when occur on an automated production line. The technician X makes an incomplete repair 1 time in 20, Y makes an incomplete repair 1 time in 10 and Z makes an incomplete 1 time in 15. For the next breakdown a repair made was found to be incomplete, find the probability that this repair was made by technician
(i) X,
(ii) Y, and
(iii) Z
The daily consumption of milk in a city, in excess of 20,000 litres, is approximately distributed as a gamma variate with parameters r = 2 and λ = 1/10,000. The city has a daily stock of 30,000 litres. What is the probability that the stock is insufficient on a particular day?