# Answer to Question #4358 in Statistics and Probability for Karren

Question #4358

Assume that the random variables X represents the number of heads that occur when a coin is tossed 4 times. Derive the probability distribution f of X

Expert's answer

Let Pi=P{X=i}.

If we toss a coin 4 times, we can get 2*2*2*2=16 different

results.

i=0:

No heads occured. The only situation satisfies this

condition: TTTT, T - tail.

So, P0=1/16.

i=1:

4 results from 16 sutisfy

this condition: HTTT, THTT, TTHT, TTTH.

So, P1=4/16=1/4.

i=2:

6 results

sutisfy this

condition.

P2=6/16=3/8

i=3:

P3=4/16=1/4

i=4:

P4=1/16

i>4:

Pi=0.

So,

the probability distribution of X is:

1/16, 1/4, 3/8, 1/4, 1/16, 0, 0,

...

If we toss a coin 4 times, we can get 2*2*2*2=16 different

results.

i=0:

No heads occured. The only situation satisfies this

condition: TTTT, T - tail.

So, P0=1/16.

i=1:

4 results from 16 sutisfy

this condition: HTTT, THTT, TTHT, TTTH.

So, P1=4/16=1/4.

i=2:

6 results

sutisfy this

condition.

P2=6/16=3/8

i=3:

P3=4/16=1/4

i=4:

P4=1/16

i>4:

Pi=0.

So,

the probability distribution of X is:

1/16, 1/4, 3/8, 1/4, 1/16, 0, 0,

...

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