Math Answers

Let X denote the random variable distribution that gives 2,3,4,5,6,7,8,9 and 10 in a deck

of cards. Find the probability of X.

A population consists of the numbers 3,5,9,10 and 6. Given the sample size of 3 Determine the following:

A. List all the possible samples

B. Compute the mean of each sample.

C. Construct the sampling distribution

D. Consryya histogram

E. Compute the mean of the sampling distribution of the sample means

F. Compute of the variance sampling distribution of the sample means

𝑓(𝑥) = 2𝑥^3 + 𝑐𝑥^2 + 2𝑥

Suppose 𝑓 is differentiable on ℝ and has two roots. Show that 𝑓′ has at least one root.

The quantity produced daily at the ABC cement factory is approximately normally

distributed with mean 0.82 and standard deviation 0.14. The units are on millions of tons.

Find the probability that the total production will between 0.80 and 0.85 million tons.

Let 𝑈 = {𝑎, 𝑒, 𝑖, 𝑜, 𝑢, 3, 6, 9, 12}, 𝐴 = {𝑜, 𝑢, 3, 12}, 𝐵 = {𝑢, 9, 6, 𝑎}, 𝑎𝑛𝑑 𝐶 = {𝑢, 12, 𝑖, 𝑜}.

1. Find 𝐶 ∪ 𝐴

2. Find (𝐶′ ∩ 𝐵) ∪ 𝐶

3. Find {(𝐵′ ∪ 𝐴)′ − 𝐴 ∪ (𝐵 ∩ 𝐵′)}

In 15 experiments studying electrical behavior of single cells 11 use microelectrodes

made of metal and the other 4 use microelectrodes made from glass tubing. If 2 of the

experiments are to be terminated for financial reasons and they are selected at random.

What are the probabilities that

a. Neither uses microelectrodes made from glass tubing?

b. Only one use microelectrodes made from glass tubing?

A. Let L: R3 R3 be defined by L([u₁ u₂ u3]) = [u₁ + 1, 2u₂]. Is L a linear transformation?

B. Let L: R₂ → R₂ be defined by L([u₁ u₂]) = [2u1 2u₂]. Is L a linear transformation?

3. Let L: R₂ → R₂ be the linear transformation defined by L ([u¹, u₂]) = [u1, 0]

a. Is [0, 2] in Ker L?

b. Is [2,2] in Ker L?

C. Is [3,0] in range L?

d. Is [ 3,2] in range L?

e. Find Ker L.

£. Find Range L.

The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days.

About what percent of the products last between 12 and 15 days?

Make a truth table to determine the logical equivalence of the statements.

1. ~ P → Q ↔ P ∨ Q
2. ~ (P → Q) ↔ P ∨ ~Q.