Math Answers

Suppose a population is composed of only 3 measures: 1, 2, and 3. The possible samples of size 2 can be draw from this population. List all the possible sample size 2 when repetition is allowed or with replacement.

Using the numbers 2, 5, 7, 8, and 9 as the elements of the population, do the following:

Find the mean of the samples of size 2 (n=2)

Construct the sampling distribution of the sample means (SDSM).

Create a graph of the histogram of the SDSM. 

Compute the Mean, Variance, and Standard Deviation of the SDSM.

1. Let p and q be the propositions.

p: It is below freezing.

q: It is snowing.

Express each of these propositions in complete English sentences.

a) p ∧ q 

b) p ∧ ¬q 

c) ¬p ∧ ¬q 

d) q ∨ p 

e) p → q 

f) q ∧ ¬p 

g) q → p 

2. Solve the following.

a) Construct a truth table.

¬p ∧ ( p ↔ ¬q )

b) Construct a truth table.

p → ( q ∧ r )

c) Construct a truth table.

( p → q ) ∨ ( ¬p ↔ r )

d) Find out if the following is a tautology, contradiction, or contingency

( p ∨ q ) ∧ ( ¬p ∧ ¬q )

e) Find out if the following propositions have logical equivalence.

( p ↔ q ) ≡ ( p → q ) ∧ ( q → p )

Jepoy has one 100-peso bill, two 200-peso bills, and five 500-peso bills in his wallet. He wants to randomly pick one bill. Let X be the random variable of choosing one bill from his wallet.

Questions:

1. Construct the probability distribution table of X. [2 points]

2. Compute for the mean of X, denoted as E(X). [2 points]

3. Interpret the mean of X. [1 point]

4. Compute for the variance of X, denoted as V(X). [5 points]

5. Compute for the standard deviation of X, denoted as SD(X). [2 points]

Interpret the standard deviation of X. [1 point

give the population 3,5,8,9, and 10. Suppose sample of size 4 are drawn from this population

.Find the minimum value of with the constraints `xy+yz+zx=3

.Find the minimum value of with the constraints `xy+yz+zx=3

show that ~p --> (q --> r ) and q --> (p v r) are logically equivalent