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(Q.1Q.2) The number of cars arriving at ICICI bank drivein window during 10min period is Poisson random variable X with b=2.1.
Q. The probability that more than 3 cars will arrive during any 10 min period is
Evaluate 1 – P(x = 0) – P(x = 1) – P(x = 2) – P(x = 3).
Evaluate P(x = 0).
(Q.3Q.5) Delhi averages three murder per week and their occurrences follow a Poisson distribution.3.
Q. The probability that there will be five or more murder in a given week is
P(5 or more) = 1 – P(0) – P(1) – P(2) – P(3) – P(4) = 0.1847.
On the average, how many weeks a year can Delhi expect to have no murders ?
P(0) = 0.0498. Hence average number of weeks per year with no murder is 52 x P(0) = 2.5889 week.
How many weeds per year (average) can the Delhi expect the number of murders per week to equal or exceed the average number per week?
P(3 or more) = 1 – P(0) – P (1) – P(2) = 0.5768. Therefore average number of weeks per year = 52 x 0.5768 or 29.994 weeks.
(Q.6Q.8) The random variable X is defined by the density f(x) = 0.5u(x) e(0.5x)6.
Q. The expect value of g(x) = X3 is
Solve E[g(x)] = E[X^{3}].
Solve integral (x f(x) dx) from negative infinity to x.
Variance is given by E[X^{2}30] – 1/16.
(Q.9Q.10) A joint sample space for two random variable X and Y has four elements (1,1), (2,2), (3,3) and (4,4). Probabilities of these elements are 0.1, 0.35, 0.05 and 0.5 respectively.
Q. The probability of the event{X 2.5, Y 6} is
The required answer is given by Fxy(2.5, 6.0) = 0.1 + 0.35 = 0.45.
The probability of the event that X is less than three is
The required answer is given by Fx(3.0) = Fxy(3.0, infinity) = 0.1 + 0.35 + 0.05 = 0.50.
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