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The ends of P and Q of a rod have the temperature at 30C and 80C until steady state situations prevail the temperature of the ends are changed to 30 C and 60 C respectively find the temperature distribution in the rod time
A Research Director of a certain university wants to replicate the result of the study 10 years ago with a standard deviation of 0.14. He wants to estimate the population mean to within an error of 0.04 of its true value. Using 95% confidence level, what is the sample size that he needs?
Let X, Y be independent and identically distributed random variables from a distribution having probability density function
f(y) = 10(1 − y)^9 , 0 < y < 1
Further let Z be the smaller value of the two random variables. Using the distribution function technique, find the probability density function of Z.
Let X, Y be independent and identically distributed random variables, each having the distribution f(x) = 5(1 − x) 4 , 0 < x < 1.
Further let W = min(X, Y) . Find the probability density function of W and hence compute the mean of W.
The joint probability density of X, Y is
f(x, y) = e −(x + y) xi > 0 i = 1, 2
0 otherwise
Using the change of variable technique, determine the joint distribution of Z = X and W = X + Y
Suppose that X1 and X2 have the joint probability distribution
f(x1, x2) = kx1x2 x1 = 1, 2, 3 x2 = 2, 3, 4
0, otherwise
Find the value of k so that the two variables are independent of each other
Let X, Y be independent and identically distributed random variables, each having Poisson distribution with rate parameter λ. Find the probability generating function of W = X + Y and hence the mean and variance of W
1) The jdf of the random variables X, Y is given as
f(x, y) = { 2 /5 (2x + 3y), 0 < x < 1, 0 < y < 1
0, elsewhere
find Pr [ 1 /3 < X < 2 /3 |y > 3 /4 ]
A population consists of the four measurements as follow:
5 9 10 8
What is the mean and standard deviation of the population?
Question Two
A company has five jobs to be done. The following matrix shows the return in USD of assigning i th machine (i=1,2,3,4,5) to the j th job (j=1,2,3,4,5).
Job 1 Job 2 Job 3 Job 4 Job 5
Machines 5 11 10 12 4
1
2 4 6 3 5
2
3 12 5 14 6
3
6 14 4 11 7
4
7 9 8 12 8
5
Assign jobs to the machines (utilize Hungarian method) so as to maximize the expected profit.
(10 marks)
#340153 on Dec 2023