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A bus arrives every 10 minutes at a bus stop. It is assumed that the waiting time for a particular individual is a random variable with a continuous uniform distribution. What is the probability that the individual waits more than 7 minutes?
Can you conclude that A = B if A and B are two sets
with the same power set?
Find two different linear mappings which map imz>3 onto rez>3
c) sum n=0 ^ m a n x^ n If the power series converges uniformly in ] alpha, beta[ , then so does . True or false? Justify. sum n=0 ^ infty a n (-x)^ n
a) Check whether the series where alpha in mathbb R ^ + . sum n=1 ^ infty n^ 2 x^ 5 n^ 4 +x^ 3 ,x in[0 ,a] is uniformly convergent or not,
7. In 1900, W. Y. Kevin published the article “The anticipated Error of a Mean”. In this pioneering paper, written under the pseudonym “Student,” Kevin introduced what later became known as Student’s t-distribution. Kevin used the following data set, which gives the additional sleep in hours obtained by a sample of 10 patients using laevohysocyamine hydrobromide.
1.9 0.8 1.1 0.1 −0.1
4.4 5.5 1.6 4.6 3.4
a. Obtain and interpret a 95% confidence interval for the additional sleep that would be obtained on average for all people using laevohysocyamine hydrobromide.
b. Was the drug effective in increasing sleep? Explain your answer.
A certain group of welfare recipients receives relief goods with a mean amount of Php 500.00 per week. A random sample of 75 recipients is survived and found that the mean amount of relief goods they received in a week is Php 600 and a standard decision of Php. 50.00. Test the claim at 1% level of significance is not Php 500.00 per week and assume that the population is approximately normally distributed.
Determine the following
Null and alternative hypothesis:
Critical value and rejection region:
Computed test statistic:
Conclusion:
a survey company, sws, claims that a majority of gen z voters prefer leni robredo as the next president over that of its main competitor, bongbong marcos. to test this claim 500 randomly selected people were surveyed. among them, 270 leni, 211 bbm, and 1919 could not make up their minds. determine whether there is sufficient evidence, at the 5% level of significance, to support the sws survey claim against the default that the population is evenly split in its preference. Show your calculations.
You have carried out an experiment to investigate the effect of the length of a pendulum not he time period of oscillation. Theory says that the pendulum should follow the rule:
T=2pi squarerootL/g
T is time period (seconds)
L is length of pendulum (metre)
G is acceleration due to gravity (9.81 m/s^2)
Calculate the expected percentage error in the time period calculation if your measurement is 2% high
four coins are tossed.Let Z be the random variable representing the number of heads that occurs.find the values of the random variable Z
