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#reading-10-common-probability-distributions
A probability distribution specifies the probabilities of the possible outcomes of a random variable.

If you toss a coin 3 times, the possible outcomes are as follows (where H means heads and T means tails): TTT, TTH, THT, HTT, THH, HTH, HHT, HHH.

In total, there are 8 possible outcomes. Of these:

  • Only 1 (TTT) has 0 heads occurring.
  • Three (TTH, THT and HTT) have 1 heads occurring.
  • Three (THH, HTH and HHT) have 2 heads occurring.
  • One (HHH) has 3 heads occurring.
Thus, if x = number of heads in 3 tosses of a coin, then x = 0, 1, 2 or 3.

Now, the respective probabilities are 1/8, 3/8, 3/8 and 1/8, as you have just seen. So:

p(0) = p(0 Heads) = 1/8
p(1) = p(1 Head) = 3/8
p(2) = p(2 Heads) = 3/8
p(3) = p(3 Heads) = 1/8

This is a probability distribution; it records probabilities for each possible outcome of the random variable.

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Subject 1. Basic Definitions
A probability distribution specifies the probabilities of the possible outcomes of a random variable. If you toss a coin 3 times, the possible outcomes are as follows (where H means heads and T means tails): TTT, TTH, THT, HTT, THH, HTH, HHT, HHH. In total, there are 8 possible outcomes. Of these: Only 1 (TTT) has 0 heads occurring. Three (TTH, THT and HTT) have 1 heads occurring. Three (THH, HTH and HHT) have 2 heads occurring. One (HHH) has 3 heads occurring. Thus, if x = number of heads in 3 tosses of a coin, then x = 0, 1, 2 or 3. Now, the respective probabilities are 1/8, 3/8, 3/8 and 1/8, as you have just seen. So: p(0) = p(0 Heads) = 1/8 p(1) = p(1 Head) = 3/8 p(2) = p(2 Heads) = 3/8 p(3) = p(3 Heads) = 1/8 This is a probability distribution; it records probabilities for each possible outcome of the random variable. Discrete Probability Distribution A table, graph or rule that associates a probability P(X=x i ) with each possible value x i that the discrete random variabl


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