A factory produces steel pipes in three plant with daily production volumes of 500, 1000 and 2000 units respectively from each of the plants. From the past experience it is known that the fraction of defective outputs produced by three plants are respectively 0.005, 0.008 and 0.010. If a pipe is selected at random from a day’s total production and founded to be defective, from which plant is that likely to have came?
To solve this problem, we can apply Bayes' Theorem to find the probability that the defective pipe came from a particular plant. ### Given: - The production volumes for the three plants are: - Plant 1: 500 units - Plant 2: 1000 units - Plant 3: 2000 units - The probabilities of a defective pipe from each plant are: _________ ______ ______ ______ _______ __________ ______ _________ _____ _____.
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For the given distribution:
find moment generating function, mean and variance of X.
A factory produces steel pipes in three plant with daily production volumes of 500, 1000 and 2000 units respectively from each of the plants. From the past experience it is known that the fraction of defective outputs produced by three plants are respectively 0.005, 0.008 and 0.010. If a pipe is selected at random from a day’s total production and founded to be defective, from which plant is that likely to have came?
The probability density function of a random variable X is f (x) = C | x |; Find C, and the value of x0 such that where F isthe CDF.
Let X be a binomial variate with n =100, p = .1.0 Find the approximate value of P (10 ≤ X ≤12) using:
(i) normal distribution
(ii)poisson distribution
[You may like to use the following values.
P(Z ≤ 67.0 ) = .0 7486, P(Z ≤ 0.33 ) = .0 6293, P(Z ≤ 0 ) = ]5.0
For a distribution, the mean is 10, variance is 16, the skewness sk4 is +1 and kurtosis b2 is 4. Obtain the first four moments about the origin i.e. zero. Comment upon the nature of the distribution.
If a random variable u has t - distribution with n degree of freedom, find the distribution of u2
(a) Poisson distribution is a limiting case of binomial distribution for and
(b) For two independent events A and B, if P(A) = 2.0 and P(B) = ,4.0 then (A ∩ B) = 0.6.
(c) If H0 : P ≤ 6.0 and X ~ B(n, p)n -known and p unknown and H1 :µ = µ0 where X ~ N (µ,σ2 )σ2 unknown, then H0 and H1 are simple null hypothesis.
(d) Frequency density of a class for any distribution is the ration of total frequency to class width.
(e) If X and Y are independent r.v.s with MX (t) and My (t) as their m.gf’s respectively, then Mx+y (t) Mx (t)My (t).