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mrs_skeptik [129]
3 years ago
14

6. Suppose that a fair coin is tossed 2 times, and the result of each toss (H or T) is recorded.

Mathematics
1 answer:
nekit [7.7K]3 years ago
5 0

Answer:

a) S= {HH, HT, TH, TT}

b) P(X=0) = (2C0) (0.5)^0 (1-0.5)^{2-0}= 0.25

P(X=1) = (2C1) (0.5)^1 (1-0.5)^{2-1}= 0.5

P(X=2) = (2C2) (0.5)^2 (1-0.5)^{2-2}= 0.25

And we have the following table:

X     |     0   |     1   |      2

P(X) |  0.25 |  0.5 |  0.25

Step-by-step explanation:

Let's define first some notation

H= represent a head for the coin tossed

T= represent tails for the coin tossed

We are going to toss a coin 2 times so then the size of the sample size is 2^2 = 4

a. What is the sample space for this chance experiment?

The sampling space on this case is given by:

S= {HH, HT, TH, TT}

b. For this chance experiment, give the probability distribution for the random variable of the total number of heads observed.

The possible values for the number of heads are X=0,1,2. If we assume a fair coin then the probability of obtain heads is the same probability of obtain tails and we can find the distribution like this:

P(X=0) = (2C0) (0.5)^0 (1-0.5)^{2-0}= 0.25

P(X=1) = (2C1) (0.5)^1 (1-0.5)^{2-1}= 0.5

P(X=2) = (2C2) (0.5)^2 (1-0.5)^{2-2}= 0.25

And we have the following table:

X     |     0   |     1   |      2

P(X) |  0.25 |  0.5 |  0.25

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All the answers to the given parts are mentioned below -

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