Maths Question

Q1 : Two fair dice are thrown. Let the random variable X be the smaller of the two scores if the scores are different, or the score on one of the dice if the scores are the same.

Find the probability distribution of X.

Q2 : In a competition, people pay $1 to throw a ball at a target. If they hit the target on the first throw they receive $5. If they hit it on the second or third throw they receive $3, and if they hit it on the fourth or
fifth throw they receive $1. People stop throwing after the first hit, or after 5 throws if no hit is made. Mario has a constant probability of 1/5 of hitting the target on any throw, independently of the results ofother throws.

(i) Mario misses with his first and second throws and hits the target with his third throw. State how much profit he has made.

(ii) Show that the probability that Mario's profit is $0 is 0.184.

(iii) Draw up a probability distribution table for Mario's profit.

(iv) Calculate his expected profit.

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I was teaching my students about probability and this question is interesting!! Then, I tried to explain WHY I never will buy4-digit because the odds against us ... BUT BUT BUT ... we could see MANY of them queueing up to buy 4-D(or these gambling games) EVERY WEEK, either BJToto, Magnum, Pan, 88 etc etc. Look ... if you know how to calculate expected PROFITS from such a game, you will understand it is a HOPE analysis game.

Which bring us to stock markets!! MANY going into markets with THESE MENTALITY --- hoping to srike it BIG. Yup, no need knowledge or what-s0-ever, just GAMBLE ma ... queue to buy with a HOPE.

Tell me this : HOW could BJToto consistently giving good dividends? HOW? This is an almost a sure-win business for the companies with gamblilng-license. Simple logic ... they apply probability and expected profits concepts!! Hey, many of my students going to study 'actuarial science' and they will be WORKING for these companies, employ a good brain to make profit from them!! Of coz, many working in insurance or finance companies too. These are brightest of brain our country could produce with our pathetic education system, ok? Many more brainy students migrated, of coz.

Tell me this : How many of these 4-D game punters will WIN money, eventually? And win it big? Take a guess of the probability??! If you DONT know what chances are there, you should NOT be in the game --- like in stock market!! Chances of us LOSING is SO GREAT ... and almost near to impossible that u will turn into millionaire winning 4-D. Perhaps, you need 7-D tickets to have HIGHER hope of becoming over-night millionaires!! Wait a minute, if you cant strike with 4-D, what are your chances that you strike it with 7-D? Dont know? Hmmm ...

If you cant even profit from CIMB as a stock, for example ... what are the chances that you know how to trade UOADev, for example? By the way, UOADev flying off another 6% today, and CIMB up 0.42% today. Checking your simple LOGIC common-sense which you have THROWN out of the window for loooong time, ever since you are in markets. Somehow, you will tell yourself ... this time it will be DIFFERENT?? How could things change so fast? You mean ... err ... you will kick your gambling habits which with ou for years in days? Hmm ... logical to you?

By understanding trading vs investing AND speculating vs punting ... is important.

If you are investing, you wont put your money in FD. That is NOT investing ... that is to play safe and keep your money savely in the bank. OK OK ...congrats to you for being a good saver. MANY in us DO NOT even have savings. I have wrote about this before!! Investing ... perhaps, shifting into good dividend stocks, diversify a little into bonds or property and some into gold. You dont need to see markets much ... perhaps, ou may like a business-model of a growing company and might want to INVEST into this particular stock(may be un-popular at the moment) as you see its potential. We invest into something we think it is traded under its 'actual' value. That is called value investing, with growth possibilities. Even that, we still monitor its developments and such. Do I need to elaborate on such basic COMMON sense?

But, if you are trading ... you have set of technical rules with you, you may add some fundamentals into it to trade ... and also checking on some indicators which you think could be used or applied. Fine. Then, you execute the plan with some system which designed or planned. Then, you patiently wait for the plan to un-fold ... checking on its reliability of the system and such. You do check your trades more often than investors. Do I need to elaborate too? COMMON sense is not there for many of us, anyway.

Speculating could be an interesting play ... you listen to certain rumours about election, about some share-holders buying or some blogs talking about the latest hot-stocks. You went to forum, chatting with your firends about certain movement of stocks. You wonder if you should take a position tmr or so, asking around more to CONVINCE your guts-feeling. You are in search of answers relating to the hot-stocks. You checked with your remisier, trusted friends and talk about it. Then, yes ... it confirmed your 'intuition' about it. I told you so ... playing in mind.

You have profitted from XXX before, you feel lukcy, you feel good ... whack into XXX tmr. In one day, you gained 12% and you know you are smart to get out in the nick of time!! It drops after that ... but but ... suddenly, three days later ... it shoots another 25%, you will be cursing yourself for selling too early, you emotion in play and yes ... repeating the process of asking around ... and should you buy XXX back as it is shooting the sky now? You cannot tahan the PAIN of missing the boat, and your PAIN of recent sale of XXX ONLY profitted 12%, your friends were laughing at you ... I told you not to be so chicken la, XXX will shoot another 50% from here. Keep it ... but you were reading another piece of news about XXX, you read from a blog stating its 'bad' situation ... you have doubt in your coming trades tmr. You moved in tmr anyway, damn ... damn ... it is down after that.

You frantically called your friend to justify your buyings .. the BAD news is going to be out, according to your remisier ... damn damn ... you hp full with sms and you are busy working!! DAMN IT ... sell-sell-sell ... for a loss. It dived all the way 15% lower ... you were patting your own shoulder ... I am smart, luckily I sold for ONLY 10% losses. You went for lunch ... DAMN IT .. it shot up another 35%. I CANT TAKE THIS ANYMORE. ...

But ... you know what, you start the WHOLE situation AGAIN, for YYY. Hmm ... strange emotion in play ... DOW up or down becoming so much of your concern. Hmm ... how to sleep ar?




Gambling ... XXX vs YYY. One is my friend working there telling you that their profits is huge and reports coming out soon(insider's tips), another is your remisier giving you the tips-of-the-year. So, un-decided without knowledge, you flip a coin. Head = XXX, Tail = YYY. We do assume that the coin is not biased with Pb(head) = Pb(tail). After buying ... when do you sell? Throw a dice ... if it is odd, then multiply with 3 but if it is even, then plus with 3. That is the number of days you are going to hold to the stock you just bought. SELL if profit, otherwise ....be a long term investor(LOL). Money management? Hmm ... Throw the dice again ... if 1 = 10%, 6 = 60% ... that is the amount you are going to use in your buying of this stock.

Example : I got RM100k in hand. I want to buy XXX @ RM0.50 or YYY@ RM0.75 per unit.

Step 1 : I will toss the dice. Lets say I got #3 ... so, I shall allocate RM30k for the stock.

Step 2 : Flip the coin --- head, I will buy XXX @0.50 or tail, I shall grab YYY@ 0.75

Step 3 : Claculate the amount of units I could buy. If I am buying XXX, I could buy 60k units but if I am buying YYY, then I could only buy 40k units. Fine.

Step 4 : Toss the dice again --- say I get #5 which is an odd number ... I shall multiply with 3. Hence, I will hold the stock for 15 days.

Step 5 : If it goes above my purchase price, sell for profits. If below my price, keep and repeat step 4 and step 5 again(a loop).

Step 6 : Repeat step-1 for the remaining capitals until RM100k being fully "INVESTED".

Talking about creativity!! Haha



Joke : This is one of my creative student drawn for a physic question. Haha. So, I asked one of my student to take a picture and send me the pix thru facebook. Haha

TEH