Create and conduct an experiment with at least five outcomes. Next, demonstrate what the experiment is and create a probability distribution.
Can this be typed out? It's for a discussion board.
Experiment name- An exp. consist of 3 independent tosses of a fair coin.
Defined random variable: (a) X: the no. of Heads
(b) Y: the no. of Heads Run(i.e consecutive occurrence of at least 2 heads)
Sample space:
HHH |
HHT |
HTH |
HTT |
THH |
THT |
TTH |
TTT |
Now,
s.n | (elementry | events) | X | Y |
1 | HHH | 3 | 1 | |
2 | HHT | 2 | 1 | |
3 | HTH | 2 | 0 | |
4 | HTT | 1 | 0 | |
5 | THH | 2 | 1 | |
6 | THT | 1 | 0 | |
7 | TTH | 1 | 0 | |
8 | TTT | 0 | 0 | |
Prob. distribution of X:
R.V X can take values 0,1,2,3 thus from the above table we can compute prob. as follows:
X=x | 0 | 1 | 2 | 3 |
p(x) | 1/8 | 3/8 | 3/8 | 1/8 |
Prob. dist. of Y:
R.V Y can take value 0,1 thus from the above table we can compute prob. as follows:
Y=y | 0 | 1 |
p(y) | 5/8 | 3/8 |
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