Suppose you toss a fair coin 4 times. Let X= the number of...

Suppose you toss a fair coin 4 times.
Let $X=$ the number of heads you get.
(a) Find the probability distribution of $X .$
(b) Make a histogram of the probability distribution.
Describe what you see.
(c) Find $P(X \leq 3)$ and interpret the result.

Key Concepts

Cumulative Probability

Cumulative probability, in this context, refers to the probability that the random variable X is less than or equal to a certain value. It is calculated by summing the probabilities of obtaining outcomes up to that value, which helps in understanding the likelihood of obtaining a count of heads within a specified range.

Binomial Distribution

This is a discrete probability distribution that describes the number of successes in a fixed number of independent trials, each with the same probability of success. In the context of tossing a fair coin, each toss is an independent trial with a success probability (getting a head) of 0.5. The binomial formula uses the number of trials, the number of successes, and the probability of success to derive the probability for each possible outcome.

Random Variables

A random variable is a quantitative variable whose value is subject to variations due to chance. In this problem, X is a random variable representing the number of heads obtained in a series of coin tosses, and it can take on integer values from 0 to the total number of tosses.

Probability Mass Function (PMF)

The probability mass function gives the probability that a discrete random variable is exactly equal to some value. For a binomial random variable, the PMF is calculated using the binomial coefficient and the probabilities of success and failure, providing a complete description of the distribution of X.

Histogram

A histogram is a graphical representation of the probability distribution where the x-axis represents the possible outcomes and the y-axis represents the probabilities associated with each outcome. It provides a visual summary of the distribution, showing how the probabilities of different numbers of heads (or successes) are distributed.

Transcript

Please give Ace some feedback