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Discrete Mathematics

Discrete Probability Distributions

Binomial Distribution

         

A basketball player is practicing 3-pointers. If the probability that he successfully scores each shot is \(\frac{4}{5},\) what is the expected value of the points he scores after throwing \(100\) shots?

Note: The player scores 3 points for each successful shot.

A basketball player is practicing 3-pointers. If the probability that he successfully scores each shot is \(\frac{3}{5},\) what is the variance of the points he scores after throwing \(800\) shots?

Note: The player scores 3 points for each successful shot.

Reina throws a fair die \(16\) times. What is the sum of the expected value and variance of the number of trials where she gets a multiple of 3?

A die is thrown \(21\) times. Getting number \(4\) is considered a success. The variance of the distribution of the number of successes is \(\text{_________}.\)

The probability of success in sending a character by wireless is \( p = \frac{3}{7}. \) What is the probability that \( 2 \) characters out of \( 4 \) are sent successfully?

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