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Construct the probability distribution for the random variables described in the following situation.

Construct The Probability Distribution For The Random Variables Described In The Following Situation class=

Sagot :

Four coins are tossed. For each toss, the outcome belongs to one of the following:

{Head,Tail}

We want to count the total number of heads obtained from those 4 tosses.

Z is the random variable representing the number of heads that occur. We want to find the all possible values of Z.

Observe that, any one of the following cases may happen:

1. All the four outcomes are 'Tail'. So number of heads is 0. Hence, Z=0 in this case.

2. Any 3 of the 4 outcomes are 'Tail' and the remaining one is a 'Head' Hence, Z=1 in this case.

3. Any 2 of the 4 outcomes are 'Tail' and the remaining two are 'Head' Hence, Z=2 in this case.

4. Any 1 of the 4 outcomes is 'Tail' and the remaining three are 'Head' Hence, Z=3 in this case.

5. All the four outcomes are 'Head'. So number of heads is 4. Hence, Z=4 in this case.

Note that, the 5 cases listed above explores all possible outcomes.

Hence, the random variable Z takes any one value from {0,1,2,3,4}.

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