SOLUTION: Suppose a fair coin is tossed three times. Let X be the random variable that represents the number of heads obtained. Find the cumulative distribution function of X.

Algebra.Com
Question 1193590: Suppose a fair coin is tossed three times. Let X be the random variable that represents the number of heads obtained. Find the cumulative distribution function of X.
Found 2 solutions by yurtman, ikleyn:
Answer by yurtman(42)   (Show Source): You can put this solution on YOUR website!
**1. Determine the Probability Mass Function (PMF) of X**
* **Possible Values of X:**
* X = 0 (no heads): TTT
* X = 1 (one head): HTT, THT, TTH
* X = 2 (two heads): HHT, HTH, THH
* X = 3 (three heads): HHH
* **Probabilities:**
* P(X = 0) = 1/8
* P(X = 1) = 3/8
* P(X = 2) = 3/8
* P(X = 3) = 1/8
**2. Define the Cumulative Distribution Function (CDF)**
* The CDF, denoted as F(x), gives the probability that the random variable X is less than or equal to a specific value (x).
**3. Calculate the CDF for Each Possible Value of X**
* **F(x) = P(X ≤ x)**
* F(x) = 0 for x < 0
* F(x) = P(X = 0) = 1/8 for 0 ≤ x < 1
* F(x) = P(X = 0) + P(X = 1) = 1/8 + 3/8 = 1/2 for 1 ≤ x < 2
* F(x) = P(X = 0) + P(X = 1) + P(X = 2) = 1/8 + 3/8 + 3/8 = 7/8 for 2 ≤ x < 3
* F(x) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 1/8 + 3/8 + 3/8 + 1/8 = 1 for x ≥ 3
**Therefore, the cumulative distribution function (CDF) of X is:**
* F(x) = 0 for x < 0
* F(x) = 1/8 for 0 ≤ x < 1
* F(x) = 1/2 for 1 ≤ x < 2
* F(x) = 7/8 for 2 ≤ x < 3
* F(x) = 1 for x ≥ 3
Answer by ikleyn(52797)   (Show Source): You can put this solution on YOUR website!
.

The answer in the post by the other tutor is incorrect and is written in absurdist form.

In this problem, the random variable X has the values 0, 1, 2, 3.

The right form for the cumulative distribution function in this problem is 

    F(x) = 1/8  for x = 0;

    F(x) = 1/2  for x = 1;

    F(x) = 7/8  for x = 2;

    F(x) =  1   for x = 3.



RELATED QUESTIONS

A fair coin is tossed four times, let x be a random variable representing the number of... (answered by mathmate)
A fair coin is tossed three times. Let X be the number of heads in the tosses minus the... (answered by Edwin McCravy)
A fair coin is tossed 10 times. Let X denote the number of heads obtained. Find the... (answered by ewatrrr)
Let x be the absolute difference between the number of heads and the number of trials... (answered by stanbon)
a fair coin is tossed four times, let x be the product of the number of heads times the... (answered by stanbon)
Let random variable x represent the number of heads when a fair coin is tossed three... (answered by Edwin McCravy)
Let random variable x represent the number of heads when a fair coin is tossed three... (answered by rothauserc)
A fair die is rolled and a fair coin is tossed. The random variable X is defined as the... (answered by Fombitz)
A fair die is rolled and a fair coin is tossed. The random variable X is defined as the... (answered by robertb)