A bag contains 5 balls which are numbered from 1 to 5. Two balls are drawn without replacement from this. Find the expectation of the sum of the numbers on these balls.
As the 5 Balls are numbered 1,2,3,4,5 & two balls are drawn without replacement
Therefore the expected Sum of the numbers on these balls are
(1,2) =
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A bag contains 5 balls which are numbered from 1 to 5. Two balls are drawn without replacement from this. Find the expectation of the sum of the numbers on these balls.
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
A smoke-detector system uses two devices A and B. If smoke is present the probability that it will be detected by device A is 0.95; by device B, 0.98 and by both devices, 0.94. If smoke is present find the probability that it will be detected
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 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?
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.
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