Respuesta :
Answer:
a) [tex]S= {HH, HT, TH, TT}[/tex]
b) [tex]P(X=0) = (2C0) (0.5)^0 (1-0.5)^{2-0}= 0.25[/tex]
[tex]P(X=1) = (2C1) (0.5)^1 (1-0.5)^{2-1}= 0.5[/tex]
[tex]P(X=2) = (2C2) (0.5)^2 (1-0.5)^{2-2}= 0.25[/tex]
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 [tex]2^2 = 4[/tex]
a. What is the sample space for this chance experiment?
The sampling space on this case is given by:
[tex]S= {HH, HT, TH, TT}[/tex]
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:
[tex]P(X=0) = (2C0) (0.5)^0 (1-0.5)^{2-0}= 0.25[/tex]
[tex]P(X=1) = (2C1) (0.5)^1 (1-0.5)^{2-1}= 0.5[/tex]
[tex]P(X=2) = (2C2) (0.5)^2 (1-0.5)^{2-2}= 0.25[/tex]
And we have the following table:
X | 0 | 1 | 2
P(X) | 0.25 | 0.5 | 0.25
