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Let Q, and R be joint distributed random variables having joint probability density function f(Q, R) = { 1 /8 e ^−(8Q+R) , Q, R > 0
0, elsewhere
Find the probability density function of Y = 0.5(Q + R ) The joint probability density function of two random variables X1 and X2 is given by f(x1, x2) = { 8, 0 < x1 < x2 < 1
0, elsewhere
Let S = X1/x2 and V = x2 , using the change of variable technique find the joint probability density function of S and VYou are asked to find the mean and variance of a random variable Y whose distribution has probability generating function is
qr /1 − (1 − q)r. 0 < q < 1
Let S be a subset of F3 defined as S = {(x, y, z) € F3 = x +y + 2x – 1=0}. Then determine S is a subspace of F3 or not.
Suppose that X and Y have bivariate normal distribution with the probability density function f(x1, x2) = k exp − (8X^2 − 6XY − 18Y^2 ) Find (a) Pr(X + Y > 1/2) (b) the joint moment generating function of Z1 = 2X − XY and Z2 = 3X + 2YLet X,Y be a random sample from the distribution
f(x) = 1 0 < x < 1
Further let Y = max(X,Y). Using the distribution function technique,
find the probability density function of Y. Hence find its mean and variance values.
Let X1, X2 have joint probability density function
f(x1, x2) = {
1/8e
−(8x1+x2)
, x1,x2>0
0, elsewhere
Find the probability density function of Y =1/2 (X1 + X2).
Suppose the random variable Y has a normal distribution with an expected value equal to 12 and variance equal to 16. What is the value of k such as that P(X<k)= 0.25
A firm manufactures three different types of hand calculators and classifies them as small, medium, and large according to their calculating capabilities. The three types hone production requirements given by the following table
Small medium large
Electronic circuit component 5 7 10
Assembly time (n) 1 3 4
Cases 1 1 1
The firm has methyl limit of 90.000 circuit components, 30.000 hours of labor and 9000 cases. If the profit is birr 6 for the small, birr 13 for the medium and birr 20 for the large calculator, then
A. How many of each should be produced to yield maximum profit
B. What is the maximum profit?
Design a circuit that generates 9's compliment of a BCD digit. Optimize your functions, taking advantage of don't care conditions where necessary, and implement using only 2-input NOR gates.
