Example 1: Calculate the mean and variance for a random variable, X defined as the number of tails in four tosses of a coin. Also, draw the probability distribution.
Let T represents a tail and H, a head. X denotes the number of tails in four tosses of a coin. X takes the value 0, 1, 2, 3, 4.
P(X = 0) = 1⁄16, P(X = 1) = 4⁄16 = 1⁄4, P(X = 2) = 6⁄16 = 3⁄8, P(X = 3) = 4⁄16 = 1⁄4, P(X = 4) = 1⁄16
The probability distribution of X is
E(X) = Σi xipi = 1 × 1⁄4 + 2 × 3⁄8 + 3 × 1⁄4 + 4 × 1⁄16 = 8⁄4 = 2.
E(X2) = 12 × ¼ + 22 × 3⁄8 + 32 × ¼ + 42 × 1⁄16 = ¼ + 3⁄2 + 9⁄4 + 1 = 5.
So, Variance of X = V(X) = E(X2) – [E(X)]2 = 5 – 22 = 1.
Example 2: What is the meaning of probability in statistics?
Probability refers to the measuring of the probability that an event will happen in a Random Experiment. Probability is enumerated as a number between 0 and 1, where, loosely speaking, 0 denotes impossibility and 1 denotes certainty. The higher the likelihood of an event, the more prone it is that the event will take place.
Example 3: What is the relationship between probability and statistics?
Probability deals with forecasting the possibility of upcoming events, whereas statistics includes the analysis of the frequency of past events. Probability is mainly a theoretical branch of mathematics, which studies the results of mathematical definitions.
Example 4: What is the probability formula?
Probability Formulas equals to Probability = (Number of a Favorable outcome) / (Total number of outcomes) P = n (E) / n (S) Over here, P means the probability, E refers to the event and finally S refers to the sample space.
Example 5: What is the example of statistics?
Generally, we make use of a statistic to guess the value of a population parameter. For instance, the average height of the sampled students is a statistic. Thus, the same will be the average grade point average. In actual fact, any calculable quality of the sample will serve as an example of a statistic.
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