### MATH 1280 Introduction to Statistics – Discussion Unit 4 – Part 2

Madonna and child, painted by Sandro Botticelli

3 keywords in this discussion are random variables, the sample space and probability. Random variable is a function that goes from a sample space to a measurable space.

Sample space is part of a probability space. A sample space is a set of all the possible "outcomes" that may arise in an experiment.

Now, we make example to understand the concept. Let’s say that we have a coin. The coin has Head=H and Tail=T.

Then, we flipped the coin 4 times. The possible outcomes are: 2 and trials are 4.

We determine Sample Space = S = 2^4 = 16 = { HHHH, HTHH, THHH, HTHT, HHHT, HTTH, TTHH, THTH, HHTT, HHTH, TTTH, THHT, HTTT, TTTT, TTHT, THTT}

Virgin, child and angels, painted by Sandro Botticelli

Let’s say we just interest on the number of heads in four flips:
x = number of heads in four flips of a coin.
The random variable x could equal 0, 1, 2, 3, or 4.

We can determine the probability of x values by computing:
x= 0 = p(0)= probability no head = 1/16 = 0.0625
x = 1 = p(1)= probability 1 head = 4/16 = 0.25
x = 2 = p (2)= probability 2 heads = 6/16 = 0.375
x = 3 = p (3)= probability 3 heads = 4/16 = 0.25
x = 4 = p (4)= probability 4 heads = 1/16= 0.0625

By following this concept, we can determine the probability of tails too.

Finally, the sum of all the probabilities is one (1). We can prove it by adding probability of x values that is : 0.0625 + 0.25 + 0.375 + 0.25+ 0.0625 = 1

### Why 3 billion Birds Have Lost in North America?

Colorful bird, painted bunting for illustration

Scary facts showed that billion birds lost in North America during last 50 years. The number around 3 billion birds.

Of 529 species, 19 bird species lost around 50 million for each species, as reported by Cornell university recently.

Examples of species lost are following:
- red-winged blackbird
- dark-eyed junco
- sparrows
- European starling
- warblers,
- blackbirds
- finches.
- horned larks
- red-winged blackbirds
- thrushes
- swallows

The question then, Why 3 billion Birds Have Lost in North America? The answer is combination factors, but mostly relate to:
- decreasing of bird habitats
- using of pesticides that killed insects as food sources for birds
- eaten by predators such as wild cats
- accident like glass collisions
- climate changes

Habitat is great important for birds, not only to live, but also to find food, rest and raise the chicks.

Loss of habitats mainly due to agricultural expansion, and might also because of property and industry development, especially in sub urban areas.

Now, my wonder about reduction of bird population in my backyard is getting answer. 6 years ago, I saw a quite lot of birds.

In the last few years or this year around, especially during spring season, I just see couple of hummingbirds, and I did not see any woodpeckers at all.

How about you? Do you aware that less birds in your backyard or any where else?

### Why Income Annuity is Getting Favorite?

Income gap, just for illustration (credit to Vanguard)

For my international friends, in case you did not know, Income annuity is an investment to provide monthly income which last for life time.

This is a kind of guaranteed income to avoid outliving of our income. We may get income payment as policy signed. People usually get regular income in the future, especially after retirement ages.

There are two choice: fix or variable regular income. Variable may fluctuate which depend on market interest.

Then, Why Income Annuity is Getting Favorite? Here the reasons:
- filling the gap of income after retirement
- may last for life or until age of 85 (depend on policy we chose)
- no annual contribution limit, while retirement accounts of 401(k) and IRAs have limitation.

Calculation of annuity payments

For better understanding, let’s say we buy US\$ 100,000 annuity policy. How much regular monthly payment if we start to receive annuity income at age 60 years old?

We do simple calculation based on available formula or using calculator. Calculation is depending on some factors:
- the annuity market rate (offered by insurance agencies) ranges from 3.7% to 8.1%. We choose 6% for example only
- We estimated our lifespan reach 85. Thus number of period: 85 years old – 60 years old = 25.

Hence, the regular monthly payment is US\$ 651.9 (US\$ 7822.67 annually). We receive this payment for 25 years.

If we wish to get monthly payment of US\$ 1500, thus, we need to invest around US\$ 240,000.

How about if we die before receiving 25 year payment? Our spouse or kids will get the balance.

### Effect of Metabolic on Beta Cells in the Pancreas

Level of glucose in the blood (credit to HiClip)

One group of three important factors lead to damage of beta cells is the metabolic factor (please see my previous post: Could Medicines Affect on Pancreas to Produce Insulin?).

The metabolic factor includes:
- hyperglycemia (higher blood sugar level)
- glucose toxicity (glucotoxicity)
- lipotoxicity
- hypoxia

Hyperglycemia leads to glucotoxicity in which high sugar level in blood could cause death on beta cell.

Many causes to Hyperglycemia, usually (in most cases) is due to:
- food consumption (not follow diabetic plan)
- drinking (too much)
- physical activities (being less active)
- sickness
- skip taking drugs for diabetic
- not using fresh insulin
- using certain medications or negative effect of drugs which stimulate higher blood sugar level.

Hyperglycemia caused of glucotoxicity (credit to PainAssist).

Glucotoxicity is disorder due to untreated higher blood sugar condition in longer period. Disorder may damage beta cell functionally and structurally.

Damaging beta cells and insulin production relate tissues will have effect on:
- lowering insulin production
- increasing insulin resistance.

You might knew that hyperglycemia have negative effects on several organs or tissues such as blood vessels. The disturbance of blood supply to important organs may cause to:

- stroke and heart diseases risk be higher
- kidney problems
- vision harmful
- nerve problem.

Hence, controlling the blood sugar level is great deal for diabetic patients.

# The other metabolic factors are lipotoxicity and hypoxia. We will discuss these topics by next post.

### MATH 1280 Introduction to Statistics – Discussion Unit 4 – Part 1

Sandro Botticelli’s painting

Random variables are used to model situations in which the outcome, before the fact, is uncertain. One component in the model is the sample space.”

The sample space is the list of all possible outcomes (or a range of possible values). For each value in the sample space, there is an associated probability.”

The probability can either be an estimate of something that exists in the real world or it could be an exact value that comes from an ideal distribution.”

Sometimes identifying the sample space helps to remind you exactly what it is that you are measuring.”

Think of something that you might want to measure that is affected by random variation.”

Identify what you want to measure, then describe its (approximate) sample space.”

Give a rough description of the probabilities associated with those values (you can simply specify if they are all the same probability or if values in one range will be more likely than values in another range).”

Painted by Sandro Botticelli

What would you say to a person who says that he or she "knows" what the outcome of an individual observation will be (an outcome of something that has not happened yet that is subject to random error)?”

When forming your answer to this question you may give an example of a situation from your own field of interest for which a random variable can serve as a model.”

One of great paintings by Sandro Botticelli

There is no requirement to use sources from the Internet, but if you use an idea or a quotation from any source, it should be cited (such as putting the author and year at the end of the sentence and then adding a reference at the end to describe the source).”

# Please find the answer on following post: MATH 1280 Introduction to Statistics – Discussion Unit 4 – Part 2

### The oldest human Ancestor is Discovered

The face of the oldest man (credit to Daily Mail)

Many mainstream medias reported about the finding of the oldest human ancestor from Ethiopia, Africa recently.

We already knew that the 3.2 million years old Lucy was believed to be our oldest ancestor. The scientific name of Lucy is Australopithecus afarensis.

Lucy is different with ape (ancient ape) in terms of:
- start to walk on two legs
- brain
- body size
- strong jaws

The similarity that Lucy’s face is look like apes, and previously live on the trees. Even though Lucy able to walk then, but they still use their hands to hang on the trees.

Skull of the oldest human ancestor

Now, scientists found the oldest human ancestor. 3.8 million years old, Australopithecus anamensis who is older than previous discovered, Lucy.

With new finding, scientists have two hypotheses:
1. Australopithecus anamensis was Lucy’s parents. Then, Lucy had evolved to be an ancestor of Australopithecus hominins. This evolutionary line led to Homo sapiens, modern human, our selves.

2. Australopithecus anamensis had directed evolutionary line to the ancestor of Australopithecus hominins, then Homo sapiens, modern man. Lucy was not involve in this evolution process.

To find out which one is true, scientists needed to assemble reliable data of specimen from:
- different time periods
- different geographical locations
- different evolutionary trajectory.

Hope, we could settle doubt soon and understand more of our ancestors, include the way they evolved to become modern human.

### Why Consuming Trash Fish could Help Environmental Protection?

Atlantic butter fish (credit to: Iberconsa)

American favorite seafood are salmon, tuna and shrimp. They consumed about 21.7 kg (48 pound) per capita per year.

But, you might not know that these marine species are not sustainable. Their population are depletion due to many causes, few of them are:

- over fishing
- over consumed
- diseases
- environmental degeneration

Consume “trash fish” instead of favorite ones is one of ways to help reducing of commercial fish in nature.

What? Trash fish?

Atlantic butter fish dish, look delicious (credit to Roy Yamaguchi)

Trash” or waste is not what its literally mean. Trash fish, like other fish that they are rich in protein and nutritional rich too.

What we call “trash fish” is actually “by catching fish.” Not in purpose to be caught. They are abundance in market, thus, the price will be cheap.

Butter fish is one of “trash fish” which have great taste if cooked with proper recipe. The price is very cheap, less than US\$ 1.00 per pound.

Just for comparison, tuna fish worth for US\$ 30 per pound, and salmon US\$ 9.99 per pound.

However, salmon costs depend very much on:
- species
- location where it from: Alaska, Norway, Denmark or other countries
- caught in the river or ocean
- wild or aquaculture salmons.

Moreover, I myself found butter fish in an ethnic grocery. The meat is white, also called as “white tuna.” I grilled the fish sometimes. Delicious for me.

Have you eaten trash fish? What species do you eat?

### Could Medicines Affect on Pancreas to Produce Insulin?

Niacin (vitamin B3), just for illustration (credit to Shuvani)

Previous post (please read: Why Pancreas of Type 2 Diabetic Persons Produce Less Insulin?), we mentioned several factors may affect on beta cell to produce insulin in pancreas.

Factors lead to harm beta cells are distinguished at least in three groups:
- Medical or pharmacological
- Biological or metabolically
- Environmental factor

We discuss effect of medicine on beta cells in this post. Some drugs have negative effect on beta cells:
- antimicrobial drugs
- antidepressants
- Niacin (vitamin B3)
- anti seizure medicines
- HIV medicines
- Pneumonia medicine such as Pentamidine
- Glucocorticoids (asthma and rheumatic arthritis drugs)
- Statin

Statin tablets (credit to AARP)

Two medicines that got attention recently are Statin and Niacin. Both are used to lower cholesterol level in the blood.

Niacin is a supplement, mean we can buy without doctor prescriptions. It is sold not only in drug stores, but also in groceries (I saw in some groceries).

Statin is a prescription medicine. In addition to combat bad cholesterol, Statin also known for heart protection, and avoiding stroke. Unfortunately, Statin may develop risk of diabetes.

Niacin as vitamin B3, a supplement that could reduce arthritis and stimulate brain function. Proper dosage is 15 mg per day.

Negative effect of Niacin that it increases the level of sugar in the blood. Thus, It may harm beta cell, then affect on diabetes patients.

Finally, diabetes patients should aware about negative effect of any medicines. If doubt, just come and ask physicians.