Search & Filtering
Prove that "\\lim _{x\\to \\infty }\\left(\\left(\\frac{1}{\\left(x+5\\right)^2}\\right)\\right)" = inf with proper justification.
For the function f defined by f(x)= 3x − 2 over [0,1] , verify L(P, f)<=U(P, f)( where the partition P is = "\\left(0,\\frac{1}{3},\\frac{2}{3},1\\right)".
Show that the function f defined on [1,0] by f(x) = (-1)n-1 for 1/n+1 <x< = 1/n (for n= 1,2,3,...) is integrable on [0,1]
Examine the following series for convergence: "\\sum _{n=0}^{\\infty }\\left(\\frac{n-2}{2n+3}\\right)^n"
find "\\lim _{n\\to \\infty }\\left(\\frac{1}{\\left(2n+1\\right)^2}+\\frac{2}{\\left(2n+2\\right)^2}\\frac{3}{\\left(2n+3\\right)^2}\\right)+...+\\frac{3}{25n}"
An association of City Mayors conducted a study to determine the average number of times a family went to buy necessities in a week. They found that the mean is 4 times in a week. A random sample of 20 families were asked and found a mean of 5 times in a week and a standard deviation of 2. Use 5% significance level to test that the population mean is not equal to 5. Assume that the population is normally distributed.
A garment factory distributes two brands of jeans. If it is found that 75 out of 250 customers prefer brand A and that 30 out of 150 prefer brand B, can we conclude at 0.05 level of significance that brand A outsells brand B?
QUESTION ONE
Kisii sports club(KSC) is trying to decide whether or not to drill for water to solve the shortage of wat, based on past experience.
water 0.2
No water 0.8
It is possible for (KSC) to hire a firm of international consultants to carry out a complete survey of the site. KSC has used the firm many times before and has made the following estimates:
If there really is water, then there is a 95% chance that the report will be favorable.
If there is no water then there is only a 10% chance that the report will indicate that there is water.
The following additional information is also provided:
The cost of drilling is Sh.9 million.
The value of the benefits if water is found is Sh.65 million
The cost of obtaining information is Sh.3 million.
Required:
Advise the company on whether to acquire additional information from the consultants [10marks]
Compute the value of imperfect information.
A study claims that on average, male high school students spend at least 3.39 hours a day playing video games with a standard deviation of 2.05 hours. A random sample of 30 teenagers were surveyed and the results showed that these teenagers spend 4.12 hours a day playing video games.
What is the null hypothesis for the given problem?
2.1 Suppose P(A) = 0.75 and P(B) = 0.82. Find the following:
2.1.1 P (A and B) if A and B are independent. (2)
2.1.2 P (not A and not B), if A and B are independent. (2)
2.1.3 P (A and B), if A and B are mutually exclusive. (1)
2.2 Solve the following inequality. (3)
x2 - 5x + 6 ≥ 0
