Consider tossing 4 coins 4 times determine the cumulative distribution function in a tabular form of element of sample space,probability and value of random variable x(x)

Answer 1

The sample space for tossing 4 coins 4 times is {HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, THHT, HTTH, TTHH, TTTT, TTTH, TTHT, THTT, HTTT, TTTH}.

Let x be the random variable representing the number of heads obtained in each of the 4 tosses. Here, x can take values from 0 to 4.

To determine the cumulative distribution function, we first calculate the probability of each possible value of x:

- P(x=0) = 1/16
- P(x=1) = 4/16
- P(x=2) = 6/16
- P(x=3) = 4/16
- P(x=4) = 1/16

Now, we construct the cumulative distribution function table:

| x | P(X<=x) |
|---|---------|
| 0 | 1/16 |
| 1 | 5/16 |
| 2 | 11/16 |
| 3 | 15/16 |
| 4 | 1 |