Posted by **ami** on Saturday, September 29, 2012 at 6:18pm.

Suppose that you

flip a fair coin (P(H)=P(T)=1

2 ) three times and you record if it landed on heads, H, or tails,

T.

(a) What is the sample space of this experiment? What is the probability of each event?

(b) [1 pt] Let X be the number of times that you observe heads. What type of random variable is X?

(c) What is the probability distribution of X?

- Needs probability and statistics help -
**Damon**, Saturday, September 29, 2012 at 6:48pm
By the way, it is not clear to me from the wording of the question if h, t, t is the same as t, h , t or not

the first way there are 6 possible outcomes. The second way there are 8

If order does not matter

1 h h h

2 h h t

3 h t t

4 t t t

probability of each event here is 1/4

if order does matter

1 h h h

2 h h t

3 h t h

4 h t t

5 t t t

6 t t h

7 t h t

8 t h h

probability of each event here is 1/8

- stor -
**Damon**, Saturday, September 29, 2012 at 7:53pm
In the second list, listing all possible outcomes there is one way to get three heads p(3h) = 1/8

three ways of getting two heads

p(2h) = 3/8

three ways of getting 1 head

p(1h) = 3/8

one way of getting 0 heads

p (0h) = 1/8

let's look at a binomial distribution where p(h) = 1/2

n = number of trials = 3

k = number of successes (number of heads)

p(h = k) = C(n,k) p^k (1-p)^k

p(h=3) = c(3,3)(1/2)^3(1/2)^0

= 3!/[3!*0!](1/8)(1) = 1/8

p(h=1) = C(3,1)(1/2)(1/2)^2

c(3,1) = 3!/[1!(3-1)!] = 3*2/2 = 3

so

p(h=1) = 3(1/2)(1/4) = 3/8

you will find that p(h=2) = C(3,2)((1/2)^2(1/2)^1 = 3/8

etc

## Answer this Question

## Related Questions

- probability - You flip a fair coin (i.e., the probability of obtaining Heads is ...
- Math - Would you be more likely to get at least 70% tails if you flip a fair ...
- Statistics - suppose you flip a fair coin five times. which of these pairs of ...
- maths - Suppose there are 10 coins laid out in front of you. All of the coins ...
- Statistics - You are shown a coin that its owner says is fair in the sense that ...
- stats - Suppose you toss a coin 100 times and get 82 heads and 18 tails. Based ...
- Data management - A coin was tossed 1000 times in an experiment to decide ...
- Data Management Help! - A coin was tossed 1000 times in an experiment to decide ...
- math - francisco tossed the coin 10 more times. he got 5 heads and 5 tails. now ...
- to bobpursley - In my heads/tails question- why isn't it 1/6? I flip a coin ...

More Related Questions