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Probability mass function for a coin toss 
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#1
Mar612, 10:42 AM

P: 201

1. The problem statement, all variables and given/known data
A biased coin is tossed ten times. Suppose that the probability of getting heads on a single toss is p. Let X be the number of heads obtained. a)Give an algebraic formula for the probability mass function of X. b) What do you think E[X] should be. 2. Relevant equations 3. The attempt at a solution No idea. The probability mass function for a discrete random variable is: p_{X}(x)=Pr(X=x) for all x I suppose that's what they want for a), but one for this example ? No idea about b), either. It's a biased coin toss. How am I supposed to find this out here? Otherwise, it would be E[X]=0.5 


#2
Mar612, 11:29 AM

P: 40

Since they don't tell what you what the bias is, you can kind of ignore it. All you know is that the probability is p. What if you tossed a fair coin 10 times? What is the probability of getting x heads?



#3
Mar612, 11:31 AM

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RGV 


#4
Mar612, 03:00 PM

P: 74

Probability mass function for a coin toss
However, some points for you (hope you know little probability): a) 1) think of what is the probability that head is obtained once; 2) then, what is the probability that it is obtained Xtimes in 10 tosses? You will obtain pmf. b) read carefully, how the mean value is defined for discrete distributions. It is very straightforward even to guess the result. 


#5
Mar612, 07:31 PM

P: 201

I still don't know how to do b. E[X] is the expected value. 5 heads and 5 tails. 


#6
Mar612, 09:47 PM

P: 40

The probability of getting one head is p, right? What's the probability of getting two heads? Write out the different possibilities, of all the coin tosses. i.e. you can get two heads, a head or tail, a tail or head, or two heads. What are the associated probabilities for each of these conditions?



#7
Mar612, 09:58 PM

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I cannot figure out whether or not you are reading your textbook or going to class and taking notes. Something is not getting through to you. You are missing the very most basic ideas, and I have no idea how to help you. RGV 


#8
Mar712, 02:23 AM

P: 74

Now think. You have 10 tosses and say you are calculating probability that you obtain right ONE head. This means 1 head AND 9 tails. Answer the following questions: 1) What is the probability that first 1 hat and then 9 tails occur? 2) How many events 1H + 9T may happen? Remind, you can get that head in ANY toss, so you will use basic combinatorics. Then what rule applies to 2H + 8T. Very probably, you will get an idea what the final answer is. 


#9
Mar712, 12:13 PM

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#10
Mar712, 12:47 PM

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You seem to be hung up on the false notion that because there are only two outcomes, they must be equally likely. NOT TRUE! In fact, even for real coins in the real world there is evidence of bias. See, eg, the articles http://www.codingthewheel.com/archiv...irproposition and http://www.statistik.lmu.de/~helmut/Texte/Euro.pdf . As this last article points, some of the Euro coins in different countries have different amounts of bias; it also cites experimental work by Diaconis and others, pointing out the existence of bias in some actual cointossing situations. RGV 


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