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There are 3 red balls and 5 yellow balls in a box. Two balls are to be drawn with replacement. If 𝑍 is a random variable that represents the number of red marbles drawn, what are the possible values of 𝑍? *

Show that the function f defined on [0,1] by f(x)= (-1)^(n-1) for 1/(n+1) < x/n ≤ 1/n where (n=1,2,3...) is integrable on [0,1]

Test whether the series ∞Σn=0 1/(n^5+x^3) converges uniformly or not

Verify if the ISBN 978-0-760-73261-6 is valid?

Given that the mean weight of senior high school students is 65kg with a standard deviation of 10. What is the percentile rank of a student with a weight of 55 kg?


During your planning specify in your decision how many girls and boys in the family you both want to have consider also the random variable x stand for

A population consists of 6 students were given the allotted time for studying and making tasks.

The number of hours are 2, 3, 4, 5, 6 and 7.

A. Find the mean and variance of the population. (10 points)

B. Using a sample size of 5, calculate the mean (𝜇𝑥̅) of the sampling distribution of the

sample means. Compare the result to the mean of the population.


Five hundred children participated in a field demonstration. Their heights averaged 110cm with a standard deviation of 6cm.How many children belong to the upper 15% of the group?




The weights (in kg) of 11 Stem B follow a normal distribution and has a mean of 50 and a standard deviation of 5. How many students have weights greater than 57?

Find the constants c0, c1, and x1 so that the quadrature formulae given by





Roots xi





0.8611363116





0.339981436





-0.339981436





-0.8611363116







Coefficients, ci





0.3478548451





0.6521451549





0.6521451549





0.3478548451







Then use it to find an answer for the following integral





Z1^(1.6) 2x/(x²-4) dx






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