Question

Consider tossing 4 coins 4 times determine the cumulative distribution function

Answer 1

To determine the cumulative distribution function, we first need to calculate all possible outcomes from tossing 4 coins 4 times. There are 2^4 = 16 possible outcomes.

Let's list them out:

1. HHHH
2. HHHT
3. HHTH
4. HTHH
5. THHH
6. HHTT
7. HTHT
8. THHT
9. HTTH
10. TTHH
11. HTTT
12. TTTH
13. TTHT
14. THTT
15. TTTT
16. TTTT

Since each outcome has equal probability (1/16), the probability for each outcome is 1/16.

Now, we can calculate the cumulative distribution function for each outcome:

1. P(X <= 0) = 0
2. P(X <= 1) = 1/16
3. P(X <= 2) = 3/16
4. P(X <= 3) = 7/16
5. P(X <= 4) = 1

So, the cumulative distribution function for tossing 4 coins 4 times is:

P(X = 0) = 0
P(X = 1) = 1/16
P(X = 2) = 3/16
P(X = 3) = 7/16
P(X = 4) = 1