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Show that the function f: [0,1]→ R defined by
F(x) = { 2 , when x is rational
{ 3 , when x is irrational
is not riemann integrable on[0,1]
Give an example of each of the following:
i. a function with a removable discontinuity
ii. a totally discontinuous function
Check whether the sequence {an}, where
an= 1/(n+1)+1/(n+2)+..1/2n is convergent or not
The function f: R→R defined by f(x)= | x-1|+ | 3-x| is differentiable at x= 4.
True or false with full explanation
Determine the t-value based on the sample size n and a
1)n=25 a= 0.01
Df=
T-Value =
2)n=15 a= 0.025
Df=
T-Value =
Q−5:
a) An urn contains 5 red balls and 6 blue balls. A ball is drawn randomly, its colour is noted, and then the ball is replaced in the urn. If thisprocess is repeated four times:
i. What is the probability of getting two red balls and 2 blue balls?
ii. What is the probability that all 4 balls are of the same colour?
iii. What is the probability that the first red ball is drawn in the 4th trial?
b) Number plates in an Arab country consist of 3 letters (chosen from a specified set of 20 letters from the Arabic alphabet) and 4 digits (from 0 to 9).
i. Find the probability of a plate having identical letters.
ii. Find the probability of a plate having identical digits.
iii. Find the probability of a plate having consecutive digits.
A population consist of the values 2,4,6 and 8
a) List all the possible sample size 2 when drawing with replacement and compute the mean of each sample.
b)Construct the sampling distribution of the mean.
c) Compute the mean, variance and standard deviation of the sample mean then compare these with the mean, Variance and standard deviation of the population.
The production cost ,represented by Y,of a bluetooth device ,is equal to the product of labour cost (m)and number of devices (x)in addition to a constant equipment renting fee(q)
The proportion of eligible voters in the next corporation election (in tumkur) who will vote for the incumbent is assumed to be 55%. What is the probability that in a random sample of 500 voters less than 49% say they will vote for the incumbent? Write your conclusion.
A random sample of n= 21 items is taken, resulting in a sample mean x¯= 17.0 with a sample standard deviation of s= 4.9. Assume x is normally distributed and use this information and α 0.05 test the following hypotheses.
H0: μ = 16
Ha: μ ≠ 16
Determine the critical value tc and t score value t based on the sample data.
