Math Answers

A. Consider a population consisting of values (1,3,5).

1. List all the possible samples of size 2 that can be drawn from the population

with replacement.

Observation Sample X (X − μX) (X − μX)²

2. Compute for the mean of the sampling distribution of the sample means.

3. Compute for the variance of the sampling distribution of the sample means.

X f Probability

P(X)

4. Construct the probability histogram of means with replacements when n = 2.

For an electric circuit with L=0.05 henry, R=20 ohms and C=100*10^-6 farad, the applied emf is 100 volts. Prove that the charge q at time 't' is given by q(t) =0.01-e^(-200t) [0.01 cos(400t) +0.02 sin(400t) ] if initially q=0 and i=0.

Water is being poured at the rate of 2π cubic meter/min into an inverted conical tank that is 12-meter deep with a radius of 6 meters at the top. If the water level is rising at the rate of 1/6 m/min and there is a leak at the bottom of the tank, how fast is the water leaking when the water is 6-meter deep?

if x is a random variable showing the number of boys in families with 4 children

a. construct a table showing the probability distribution(probability distribution table)

b. find the E(X)

c. Find the Var(X)

find the area of the surface generated when the given arc is revolved about the y axis ( y= 4 - x^2 from x=0 to x=2 )

C. Let p and q be proposition

p: 4 is a rational number

q: √3 is an irrational number

Express each of these proposition as an English sentences:

1. ~p
2. p∨ q
3. p ∧ q
4. p → q
5. p ↔ q

Random samples of size 𝑛 = 2 are drawn from a finite population

consisting of the numbers 5,6,7,8, and 9.

a. Find the mean of the population 𝜇.

b. Find the standard deviation of the population 𝜎.

c. Find the mean of the sampling distribution of the sample means 𝜇𝑋̅.

d. Find the standard deviation of the sampling distribution of the sample

means 𝜎𝑋̅.

e. Verify the Central Limit theorem by:

I. Comparing 𝜇 and 𝜇𝑋̅.

II. Comparing 𝜎 and 𝜎𝑋̅.

Find the order and degree of the following differential equation 2(d^2y/dx^2)-3*(dy/dx)+y=0

find the order and degree of the following differential equation (d^3*y/dx^3)^2-3*(d^2*y/dx^2)+4y=0

If a finite population has four elements: 6, 1, 3, 2.

(a) How many different samples of size n = 2 can be selected from this population if you sample without replacement?

(b) List all possible samples of size n = 2.

(c) Compute the sample mean for each of the samples given in part b.

(d) Find the sampling distribution of and draw the histogram.

(e) Compute standard error.

(f) If all four population values are equally likely, calculate the value of the population mean . Do any of the samples listed in part (b) produce a value of exactly equal to mean