Food for Thought

Actuarial Food

Perplexing Weight Loss

Suppose a rare jellyfish that is 99% water (by weight) gets beached on a deserted beach. If it gets dehydrated and becomes 98% water (by weight), it would have lost 50% of its weight. True or false?

Tribute to the Liar’s Paradox

Everything I say is a lie. True or false?

Day of the week

Had yesterday been tomorrow, today would have been Friday. What day is today? Actuaries do look forward to Fridays.

Road to 24

How do you apply addition, subtraction, division, and multiplication to 3, 3, 8, 8 to get 24? Each number can only be used once. For example with 2, 2, 8, 8, we have (2 + 2) * 8 - 8 = 24. However, 3, 3, 8, 8 is considerably harder.

Half?

A risk management actuary and a pricing actuary are stuck in the Kalahari and locked in a heated and debilitating argument over whether a glass of water was half full or half empty, that old silly question (from an actuarial perspective). The risk manager, realising the risk of getting into an infinite loop based on a quick regression of pass regressive debates, decides to digress like an egress: Is this glass even half anything?

How would you determine if the water is half the volume of the glass? No measuring aids.

Airplane Seating Problem

100 actuaries, each with an assigned seat, are boarding an airplane with 100 seats going to an actuarial convention. They board the airplane in order, the first passenger, an absent-minded student, lost his ticket so he just takes a random seat. Subsequent passengers either sit in their assigned seats or, if the seat is taken, take a random empty seat. What's the probability that the last passenger would sit on his own seat?

Knotty Exam Raise

An actuarial student has just passed an exam and is rather excited about the exam raise. Her manager hands her two envelopes each with a specific salary increment, but she can only pick one. The envelopes are indistinguishable (and the manager is not giving any facial clues – awkward actuaries!), so she flips a coin a picks one envelope. The manager then tells her that the amount in one envelope is double the other and that she can swap the envelopes if she wants. What should she do?

A more seasoned actuary sets up the following process for solving the problem:

  1. Denote by Athe amount in my selected envelope.
  2. The probability that Ais the smaller amount is 1/2, and that it is the larger amount is also 1/2.
  3. The other envelope may contain either 2Aor A/2.
  4. If Ais the smaller amount, then the other envelope contains 2A.
  5. If Ais the larger amount, then the other envelope contains A/2.
  6. Thus the other envelope contains 2Awith probability 1/2 and A/2 with probability 1/2.
  7. So the expected value of the money in the other envelope is:
  8. This is greater than A, so you gain on average by swapping.

The student, just to make sure she understands the set up, then says:

  1. After the switch, I can denote that content by Band reason in exactly the same manner as you did.
  2. The most rational thing to do is to swap back again.
  3. To be rational, I will thus end up swapping envelopes indefinitely. Infinite “do loop”! We have a contradiction.

Birds and the Wire

Take a wire stretched between two posts, and have a large number of birds land on it at random. Take a bucket of yellow paint, and for each bird, paint the interval from it to its closest neighbour. The question is: what proportion of the wire will be painted. More strictly: as the number of birds goes to infinity, what is the limit of the expected value of the proportion of painted wire, assuming a uniform probability distribution of birds on the wire.

 

Actuarial Jokes

Disclaimer

We can make jokes, but we can’t write them. If any one of these jokes sounds too good to have been written by an actuary, then it wasn’t. This is not one of the jokes.

What is an actuary?

A professional who can solve a problem you didn't know you had in a way that you can't understand.

He Who Doesn’t Laugh

If you can’t get the joke, you must be an actuary, most likely a tax actuary. (So why not a lawyer, you ask? They don’t even read jokes notwithstanding how humorous said jokes written hereinafter may or might be deemed or considered as such by a reasonable person.)

Great Actuarial Choice

Two actuaries were biking across when one said: "Awesome bike, where did you get it?" The second actuary replied: "Well, I was walking along yesterday, minding my own business, when a beautiful woman rode up on this bike, threw it to the ground, took off all her clothes and said, ‘take what you want.’" The first actuary nodded approvingly and said: "Good choice; the clothes probably wouldn't have fit you anyway."

Cheating Epidemic

The problem with company actuaries is that they tend to cheat in order to get results. The problem with academic actuaries is that they tend to work on toy problems in order to get results. The problem with consulting actuaries is that they tend to cheat at toy problems in order to get results. (Just in case you are wondering, QED actuaries are advisors. )

Chickens

Why did the chicken cross the road?

Kindergarten Teacher: To get to the other side.

Physicist: To be on the same side of the Moebius strip.

Actuary: We need to perform an experience study and build a model of the frequency and duration of chicken road crossings. Poisson, Pareto, Burr, Norman Inverse Gaussian, or Gamma? It’s going to be a fun-filled weekend!

Whose Fault?

A man is flying in a hot air balloon and realises he is hopelessly lost. He sees a lady on the ground and, having swallowed his pride, asks: “Can you help me – I’m lost.” The lady replies: “You’re in a hot air balloon, about 25 metres off the ground.” The man replies: “You must be an actuary. You gave me information that is accurate, but completely useless.” The actuary retorts: “You must be in marketing.” He yells back, “yes, how did you know?” The actuary says, “well, you’re in the same situation you were in before you talked to me, but now it’s my fault.”

Loner

All the functions of x are at a party. They are all having fun, dancing and mingling except exp(x). Exp(x) is standing alone in the corner looking miserable. The other functions notice this and approach him they ask him “exp(x) why don’t you integrate with us?” and he replied “because it makes no difference!”

Favourite Dessert

Question: What is an actuary’s favourite dessert?
Answer: Pi

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