Question

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

Answer 1

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,
...