Question

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.

Answer 1

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