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A population consists of 4 number 3, 7, 11, 15 of sample size n=2 which can be drawn without replacement from the population.




a. Population mean



b. Population variance



c.population standard deviation



d. Mean of the sampling distribution of the sample means



e. Variance of the sampling distribution of the sample means



f. Standard deviation of the sampling distribution of the sample means




Determine the set of interior points, exterior points,

accumulation points, isolated points, and boundary

points of the set E = {x : x2< 2}.


suppose three coins are tossed let y be the random variable representing the number of tails that occur find the values of the random variable y make a table to illustrate the situation

1. Create an open-top box using a ΒΌ illustration board. Make sure that you


will be creating the maximum volume of a box.


2. To create a box, you will be removing a square from each corner of the box


and folding up the flaps on each side.


3. Use the concept of problems involving optimization to get the maximum


volume of the box.


4. Explain why you arrive with your final output of creating a maximum vol-


ume of an open-top box.


5. Show your solution on a short bond paper.

Let Ω be a sample space of rolling a fair die once and observing the face value.


Let A be the event with element 1 and 3. Show that the smallest 𝜎 βˆ’ 𝑓𝑖𝑒𝑙𝑑


containing A is a 𝜎 βˆ’ 𝑓𝑖𝑒𝑙d

A population consists of the numbers 2, 4, 5, 9, and 10. A random sample of size 2 is


taken from the population.


1. Compute the number of samples using combination.


2. Complete the table on the right and compute the mean Β΅, variance


Οƒ2 and standard deviation Οƒ of the population.


3. Complete the table on the right and compute


the mean ΞΌxΜ„, variance ΟƒxΜ„2


, and standard


deviation ΟƒxΜ„ of the sampling distribution of


sample means.

A population of size N=150 has u=8 and standard deviation of o=5.4. What is the probability that a random sample of size n=20 will have a mean of 9.5 above.

a meeting of envoys was attended by 4 americans and 5 filipinos. If 6 envoys were selected at random one after the other, determine the values of the random variable F representing the number of filipinos


three balls are drawn in succession without replacement from a jar containing 8 white balls and 5 black balls. Let B be the random variable representing number of black balls


You select a card from a standard deck of playing cards. Find the probability of each event.

1. Event D: Selecting the nine of clubs

2. Event E: Selecting a heart

3. Event F: Selecting a diamond, heart, club, or spade


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