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Find the mean and variance of a random variable X whose distribution has probability generating moment function is
pr / 1 − (1 − p)r 0 < p < 1
Suppose that X and Y have bivariate normal distribution with the probability density function
f(x, y ) = k e − (8x^2− 6xy − 18y^2)
Find
(a) Pr(X + Y > 1/2)
(b) the joint moment generating function of Z = 2X − Y and W = 3X + 2Y
Let X, Y independent and identically distributed random variables from a distribution having probability density function
f(x) = 1, 0 < x < 1
Further let Z = max(X, Y). Using the distribution function technique, find the probability density function of Z. Hence find its mean and variance values.
a) If a teacher wants to help learners to become proficient in mathematics, she must first of all be proficient herself. In the study guide, Kilpatrick’s (2001) five strands of mathematics proficiency are listed on page 39, on the left hand what proficiency in a learner means, and on the right side, what proficiency in a teacher means. A teacher is teaching problem solving to Grade 6 learners and she uses the following example:
+ + = +
but + + = + +
and the weighs 6 kg, what is the weight of the cylinder and the cube? In this problem, why is adaptive reasoning needed to solve the problem? Remember that in Grade 6 learners do not know yet how to work with
How would a behaviourist teacher explain 1/2÷1/3?
State the null hypothesis 𝐻0 and alternative hypothesis 𝐻𝐴 for the following experiments
2. Does fresh fruit juice have effect on colds in the group who regularly drink it compared to the group who do not?
A researcher is testing the hypothesis that all teenagers spend an average of 8 hours on their computers during the weekends. He knows that the standard deviation is 0.3 hour. He selects a sample of 144 teenagers and decides to reject the null hypothesis when the sample mean is 8.5 hours or less.
a. What us the probability of that the researcher commits a type I error?
b. If the true population mean is 7 hours, what is the probability that the he commits a type II error?
c. Determine the power of test.
11. Solve the system by using the substitution method:
y=(x+3)²-1
y=2x+5
A. (-3,-1) and (-1,3)
B. (-1,-3) and (3,-1)
C. (-3,1),(-1,3),(-1,-3) and (3,-1)
D.No solution! it is an inconsistent system
12. Solve the system by using the elimination method:
3x+y²=21
4x²-2y³=-2
A. (2,3) and (2,-3)
B. (-2,3) and (-2,-3)
C. (2,3),(2,-3),(-2,3) and (-2,-3)
D. No solution! It is an Inconsistent System
Systems Of Nonlinear Equations
-Solve the following equations.
1. { x+2y=0
{ x²+y²=5
2. { x+y=3
{ x²+y²=2
1. A hyperbola has vertices (1,9) and (14,9) and one of its foci is (-2,9) find its standard equation.
2. Determine the foci vertices and asymptote of the hyperbola with equation.
x²/16-y²/20=1
Sketch the graph and include these points and lines along with the auxiliary rectangle.
3. Give the coordinates of the foci vertices and asymptote of the hyperbola with equation 9x2-4y2-90x-32y=-305. Sketch the graph and include these and lines along 2ith auxiliary rectangle.
#339914 on Dec 2023